Datasets:

nwadgeri

/

mydata

like 0

[INST] help me answer this question Find the equation of the parabola that satisfies the given conditions: Focus (6,0); directrix x = – 6, think step by step [/INST] The focus lies on the x-axis, so the equation of the parabola is either of the form y^2 = 4ax or y^2 = -4ax. The directrix, x = -6, is to the left of the y-axis, and the focus (6, 0) is to the right of the y-axis. Hence, the parabola is of the form y^2 = 4ax. Here, a = 6. , The answer is y^2 = 24x.

<s>[INST] [INST] help me answer this question Find the equation of the parabola that satisfies the given conditions: Focus (6,0); directrix x = – 6, think step by step [/INST]</s> <s>The focus lies on the x-axis, so the equation of the parabola is either of the form y^2 = 4ax or y^2 = -4ax. The directrix, x = -6, is to the left of the y-axis, and the focus (6, 0) is to the right of the y-axis. Hence, the parabola is of the form y^2 = 4ax. Here, a = 6. , The answer is y^2 = 24x.</s>

[INST] help me answer this question The elements are odd natural numbers which are less than 10. Hence, (v) matches with (b)., think step by step [/INST] , The answer is The elements of set (iv) are odd natural numbers less than 10, which makes it match with set (b).

<s>[INST] [INST] help me answer this question The elements are odd natural numbers which are less than 10. Hence, (v) matches with (b)., think step by step [/INST]</s> <s>, The answer is The elements of set (iv) are odd natural numbers less than 10, which makes it match with set (b).</s>

[INST] help me answer this question What is the probability of getting no tail?, think step by step [/INST] , The answer is The probability of getting no tail is 1/8.

<s>[INST] [INST] help me answer this question What is the probability of getting no tail?, think step by step [/INST]</s> <s>, The answer is The probability of getting no tail is 1/8.</s>

[INST] help me answer this question Given x2/100 + y2/400 = 1, what is the length of the latus rectum?, think step by step [/INST] , The answer is Length of latus rectum = 2b2/a = (2×102)/20 = (2×100)/20 = 10

<s>[INST] [INST] help me answer this question Given x2/100 + y2/400 = 1, what is the length of the latus rectum?, think step by step [/INST]</s> <s>, The answer is Length of latus rectum = 2b2/a = (2×102)/20 = (2×100)/20 = 10</s>

[INST] help me answer this question P (k + 1) is true whenever P (k) is true., think step by step [/INST] Principle of Mathematical Induction , The answer is Therefore, by the principle of mathematical induction, statement P (n) is true for all natural numbers, i.e., n.

<s>[INST] [INST] help me answer this question P (k + 1) is true whenever P (k) is true., think step by step [/INST]</s> <s>Principle of Mathematical Induction , The answer is Therefore, by the principle of mathematical induction, statement P (n) is true for all natural numbers, i.e., n.</s>

[INST] help me answer this question Are the events A and C mutually exclusive?, think step by step [/INST] A ∩ C = {(2, 1), (2, 2), (2, 3), (4, 1)} eq φ , The answer is No, they are not mutually exclusive.

<s>[INST] [INST] help me answer this question Are the events A and C mutually exclusive?, think step by step [/INST]</s> <s>A ∩ C = {(2, 1), (2, 2), (2, 3), (4, 1)} eq φ , The answer is No, they are not mutually exclusive.</s>

[INST] help me answer this question Find the multiplicative inverse of each of the complex numbers given in Exercises 11 to 13., think step by step [/INST] , The answer is Not available in the text

<s>[INST] [INST] help me answer this question Find the multiplicative inverse of each of the complex numbers given in Exercises 11 to 13., think step by step [/INST]</s> <s>, The answer is Not available in the text</s>

[INST] help me answer this question What is the coefficient of variation (C.V) for X?, think step by step [/INST] , The answer is The coefficient of variation (C.V) for X is 11.58.

<s>[INST] [INST] help me answer this question What is the coefficient of variation (C.V) for X?, think step by step [/INST]</s> <s>, The answer is The coefficient of variation (C.V) for X is 11.58.</s>

[INST] help me answer this question The sum of the first three terms of a G.P. is 39/10, and their product is 1. Find the common ratio and the terms., think step by step [/INST] , The answer is The common ratio and the terms of the G.P.

<s>[INST] [INST] help me answer this question The sum of the first three terms of a G.P. is 39/10, and their product is 1. Find the common ratio and the terms., think step by step [/INST]</s> <s>, The answer is The common ratio and the terms of the G.P.</s>

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

<s>[INST] [INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers except `x = 4`.</s>

[INST] help me answer this question Solve the given inequality: 3x - 7 > 1, think step by step [/INST] , The answer is The solution of the given inequality is x > 10/3.

<s>[INST] [INST] help me answer this question Solve the given inequality: 3x - 7 > 1, think step by step [/INST]</s> <s>, The answer is The solution of the given inequality is x > 10/3.</s>

[INST] help me answer this question What is the perimeter of a square with a side length of 7 cm?, think step by step [/INST] A square is a special type of quadrilateral where all four sides are equal. So, when you know one side, you can find the other three. And, to find the distance around the square (perimeter), you just multiply the length of one side by 4. , The answer is The perimeter of a square is calculated by the formula 4 * side length. So, the perimeter is 4 * 7 = 28 cm.

<s>[INST] [INST] help me answer this question What is the perimeter of a square with a side length of 7 cm?, think step by step [/INST]</s> <s>A square is a special type of quadrilateral where all four sides are equal. So, when you know one side, you can find the other three. And, to find the distance around the square (perimeter), you just multiply the length of one side by 4. , The answer is The perimeter of a square is calculated by the formula 4 * side length. So, the perimeter is 4 * 7 = 28 cm.</s>

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

<s>[INST] [INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers.</s>

[INST] help me answer this question Given x2/16 + y2/9 = 1, what is the length of the minor axis?, think step by step [/INST] , The answer is Length of minor axis = 2b = 2 (3) = 6

<s>[INST] [INST] help me answer this question Given x2/16 + y2/9 = 1, what is the length of the minor axis?, think step by step [/INST]</s> <s>, The answer is Length of minor axis = 2b = 2 (3) = 6</s>

[INST] help me answer this question Find the derivative of cos x from the first principle., think step by step [/INST] , The answer is The derivative of cos x from the first principle is not provided.

<s>[INST] [INST] help me answer this question Find the derivative of cos x from the first principle., think step by step [/INST]</s> <s>, The answer is The derivative of cos x from the first principle is not provided.</s>

[INST] help me answer this question What is the difference between an Element and a Compound?, think step by step [/INST] Elements are the building blocks of matter, while compounds are formed by the chemical combination of elements. , The answer is An element is a pure substance that cannot be broken down into simpler substances by chemical means, while a compound is a substance composed of two or more elements chemically combined in a fixed proportion.

<s>[INST] [INST] help me answer this question What is the difference between an Element and a Compound?, think step by step [/INST]</s> <s>Elements are the building blocks of matter, while compounds are formed by the chemical combination of elements. , The answer is An element is a pure substance that cannot be broken down into simpler substances by chemical means, while a compound is a substance composed of two or more elements chemically combined in a fixed proportion.</s>

[INST] help me answer this question If X and Y are two sets, such that n(X) = 17, n(Y) = 23 and n(X ∪ Y) = 38, find n(X ∩ Y)., think step by step [/INST] Using the formula n(X ∪ Y) = n(X) + n(Y) – n(X ∩ Y) , we find n(X ∩ Y) = 2 , The answer is n(X ∩ Y) = 2

<s>[INST] [INST] help me answer this question If X and Y are two sets, such that n(X) = 17, n(Y) = 23 and n(X ∪ Y) = 38, find n(X ∩ Y)., think step by step [/INST]</s> <s>Using the formula n(X ∪ Y) = n(X) + n(Y) – n(X ∩ Y) , we find n(X ∩ Y) = 2 , The answer is n(X ∩ Y) = 2</s>

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

<s>[INST] [INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers.</s>

[INST] help me answer this question Is the square of every number an even number?, think step by step [/INST] The square of a number is an even number when the number is even, otherwise it's an odd number. , The answer is No.

<s>[INST] [INST] help me answer this question Is the square of every number an even number?, think step by step [/INST]</s> <s>The square of a number is an even number when the number is even, otherwise it's an odd number. , The answer is No.</s>

[INST] help me answer this question If A = {x: x is a natural number}, B ={x: x is an even natural number} C = {x: x is an odd natural number} and D = {x: x is a prime number}, find (i) A ∩ B (ii) A ∩ C (iii) A ∩ D (iv) B ∩ C (v) B ∩ D (vi) C ∩ D, think step by step [/INST] , The answer is {'i': 'A ∩ B = {2, 4, 6, 8, ...}', 'ii': 'A ∩ C = {1, 3, 5, 7, ...}', 'iii': 'A ∩ D = {2, 3, 5, 7, ...}', 'iv': 'B ∩ C = Φ', 'v': 'B ∩ D = {2}', 'vi': 'C ∩ D = Φ'}

<s>[INST] [INST] help me answer this question If A = {x: x is a natural number}, B ={x: x is an even natural number} C = {x: x is an odd natural number} and D = {x: x is a prime number}, find (i) A ∩ B (ii) A ∩ C (iii) A ∩ D (iv) B ∩ C (v) B ∩ D (vi) C ∩ D, think step by step [/INST]</s> <s>, The answer is {'i': 'A ∩ B = {2, 4, 6, 8, ...}', 'ii': 'A ∩ C = {1, 3, 5, 7, ...}', 'iii': 'A ∩ D = {2, 3, 5, 7, ...}', 'iv': 'B ∩ C = Φ', 'v': 'B ∩ D = {2}', 'vi': 'C ∩ D = Φ'}</s>

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

<s>[INST] [INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers except `x = 4`.</s>

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

<s>[INST] [INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers except `x = 4`.</s>

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

<s>[INST] [INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is `x ≥ 1`.</s>

[INST] help me answer this question Foci (±3, 0), a = 4. What is the equation of the ellipse?, think step by step [/INST] The foci are on the x-axis, so the major axis is along the x-axis. The equation of the ellipse will be of the form x2/a2 + y2/b2 = 1. Since the foci are (±3, 0), c = 3 and a = 4. Using the formula a2 = b2 + c2, we get b2 = 7. Therefore, the equation of the ellipse is x2/16 + y2/7 = 1. , The answer is The equation of the ellipse is x2/16 + y2/7 = 1.

<s>[INST] [INST] help me answer this question Foci (±3, 0), a = 4. What is the equation of the ellipse?, think step by step [/INST]</s> <s>The foci are on the x-axis, so the major axis is along the x-axis. The equation of the ellipse will be of the form x2/a2 + y2/b2 = 1. Since the foci are (±3, 0), c = 3 and a = 4. Using the formula a2 = b2 + c2, we get b2 = 7. Therefore, the equation of the ellipse is x2/16 + y2/7 = 1. , The answer is The equation of the ellipse is x2/16 + y2/7 = 1.</s>

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

<s>[INST] [INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers except `x = 4`.</s>

[INST] help me answer this question How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5, assuming that Repetition of the digits is allowed?, think step by step [/INST] N/A , The answer is 125

<s>[INST] [INST] help me answer this question How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5, assuming that Repetition of the digits is allowed?, think step by step [/INST]</s> <s>N/A , The answer is 125</s>

[INST] help me answer this question The area (ABCD) = 29 + 63/2 units², find the area of the figure., think step by step [/INST] The area of the figure ABCD is the sum of 29 and 63/2, which is 121/2 units². , The answer is The area of the figure is 121/2 units².

<s>[INST] [INST] help me answer this question The area (ABCD) = 29 + 63/2 units², find the area of the figure., think step by step [/INST]</s> <s>The area of the figure ABCD is the sum of 29 and 63/2, which is 121/2 units². , The answer is The area of the figure is 121/2 units².</s>

[INST] help me answer this question The remaining 10 places can be filled with 10 remaining letters. Find the number of permutations., think step by step [/INST] , The answer is No. of permutations = 14 × 10!/4! = 25401600

<s>[INST] [INST] help me answer this question The remaining 10 places can be filled with 10 remaining letters. Find the number of permutations., think step by step [/INST]</s> <s>, The answer is No. of permutations = 14 × 10!/4! = 25401600</s>

[INST] help me answer this question Given x2/49 + y2/36 = 1, what is the length of the latus rectum?, think step by step [/INST] , The answer is Length of latus rectum = 2b2/a = (2×62)/7 = (2×36)/7 = 72/7

<s>[INST] [INST] help me answer this question Given x2/49 + y2/36 = 1, what is the length of the latus rectum?, think step by step [/INST]</s> <s>, The answer is Length of latus rectum = 2b2/a = (2×62)/7 = (2×36)/7 = 72/7</s>

[INST] help me answer this question Substitute the value of b² in equation (4), 1/a² = 1/16(1 – 9/b²)., think step by step [/INST] , The answer is a² = 52

<s>[INST] [INST] help me answer this question Substitute the value of b² in equation (4), 1/a² = 1/16(1 – 9/b²)., think step by step [/INST]</s> <s>, The answer is a² = 52</s>

[INST] help me answer this question What is the inequality for the relationship between the third piece and the second piece?, think step by step [/INST] , The answer is 2x ≥ (x+3) + 5

<s>[INST] [INST] help me answer this question What is the inequality for the relationship between the third piece and the second piece?, think step by step [/INST]</s> <s>, The answer is 2x ≥ (x+3) + 5</s>

[INST] help me answer this question (2n +7) < (n + 3)2, think step by step [/INST] N/A , The answer is The given statement is true for all natural numbers n.

<s>[INST] [INST] help me answer this question (2n +7) < (n + 3)2, think step by step [/INST]</s> <s>N/A , The answer is The given statement is true for all natural numbers n.</s>

[INST] help me answer this question sin 4x = 4 cos2 x sin 4x - 8 cos4 x sin4 x + 4 cos6 x sin4 x, think step by step [/INST] The given expression is incorrect, and it should be cos 4x = 1 - 8 cos2 x sin2 x. , The answer is False

<s>[INST] [INST] help me answer this question sin 4x = 4 cos2 x sin 4x - 8 cos4 x sin4 x + 4 cos6 x sin4 x, think step by step [/INST]</s> <s>The given expression is incorrect, and it should be cos 4x = 1 - 8 cos2 x sin2 x. , The answer is False</s>

[INST] help me answer this question The number of ways we can select a team of 11 players where 4 players are bowlers from 17 players is , think step by step [/INST] N/A , The answer is 3960

<s>[INST] [INST] help me answer this question The number of ways we can select a team of 11 players where 4 players are bowlers from 17 players is , think step by step [/INST]</s> <s>N/A , The answer is 3960</s>

[INST] help me answer this question 2 (2x + 3) – 10 < 6 (x – 2), think step by step [/INST] The solutions of the given inequality are defined by all the real numbers greater than 4. Hence, the required solution set is (4, ∞). , The answer is x > 4

<s>[INST] [INST] help me answer this question 2 (2x + 3) – 10 < 6 (x – 2), think step by step [/INST]</s> <s>The solutions of the given inequality are defined by all the real numbers greater than 4. Hence, the required solution set is (4, ∞). , The answer is x > 4</s>

[INST] help me answer this question From equations (i) and (ii), what is the solution of given inequalities?, think step by step [/INST] , The answer is The solution is (-7, 11).

<s>[INST] [INST] help me answer this question From equations (i) and (ii), what is the solution of given inequalities?, think step by step [/INST]</s> <s>, The answer is The solution is (-7, 11).</s>

[INST] help me answer this question A point is on the x-axis. What are its y-coordinate and z-coordinates?, think step by step [/INST] , The answer is If a point is on the x-axis, then the coordinates of y and z are 0.

<s>[INST] [INST] help me answer this question A point is on the x-axis. What are its y-coordinate and z-coordinates?, think step by step [/INST]</s> <s>, The answer is If a point is on the x-axis, then the coordinates of y and z are 0.</s>

[INST] help me answer this question In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?, think step by step [/INST] Total number of letters in MISSISSIPPI = 11. Number of permutations = 11! / (4! * 4! * 2!) = 39,916,800 / (24 * 24 * 2) = 34,650. Number of permutations where the four I’s come together = 840. Therefore, the total number of permutations where the four I’s don't come together = 34,650 - 840 = 33,810. , The answer is The number of permutations where the four I’s do not come together is 33,810.

<s>[INST] [INST] help me answer this question In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?, think step by step [/INST]</s> <s>Total number of letters in MISSISSIPPI = 11. Number of permutations = 11! / (4! * 4! * 2!) = 39,916,800 / (24 * 24 * 2) = 34,650. Number of permutations where the four I’s come together = 840. Therefore, the total number of permutations where the four I’s don't come together = 34,650 - 840 = 33,810. , The answer is The number of permutations where the four I’s do not come together is 33,810.</s>

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

<s>[INST] [INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers except `x = 4`.</s>

[INST] help me answer this question (ii) q: The center of a circle bisects each chord of the circle., think step by step [/INST] The given statement is false. The center of a circle does not bisect every chord of the circle. A chord that passes through the center of the circle is called a diameter, and it bisects the circle into two equal parts. However, not all chords have their midpoints at the center of the circle. , The answer is False.<br>The center of a circle does not bisect every chord of the circle.<br>A chord that passes through the center of the circle is called a diameter. A diameter is the longest chord of a circle, and it bisects the circle into two equal parts. However, not all chords have their midpoints at the center of the circle.

<s>[INST] [INST] help me answer this question (ii) q: The center of a circle bisects each chord of the circle., think step by step [/INST]</s> <s>The given statement is false. The center of a circle does not bisect every chord of the circle. A chord that passes through the center of the circle is called a diameter, and it bisects the circle into two equal parts. However, not all chords have their midpoints at the center of the circle. , The answer is False.<br>The center of a circle does not bisect every chord of the circle.<br>A chord that passes through the center of the circle is called a diameter. A diameter is the longest chord of a circle, and it bisects the circle into two equal parts. However, not all chords have their midpoints at the center of the circle.</s>

[INST] help me answer this question What is D – E?, think step by step [/INST] , The answer is The value of D – E is (1, 2, 3).

<s>[INST] [INST] help me answer this question What is D – E?, think step by step [/INST]</s> <s>, The answer is The value of D – E is (1, 2, 3).</s>

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

<s>[INST] [INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers except `x = 4`.</s>

[INST] help me answer this question What are the possible outcomes when a coin is tossed?, think step by step [/INST] , The answer is The possible outcomes when a coin is tossed are Head (H) or Tail (T).

<s>[INST] [INST] help me answer this question What are the possible outcomes when a coin is tossed?, think step by step [/INST]</s> <s>, The answer is The possible outcomes when a coin is tossed are Head (H) or Tail (T).</s>

[INST] help me answer this question Solve the quadratic equation x2 + 3 = 0, think step by step [/INST] Comparing the given equation with ax2 + bx + c = 0, we have a = 1, b = 0, and c = 3. The discriminant (D) is calculated as D = b2 - 4ac = 02 - 4 × 1 × 3 = -12. Since D < 0, the roots of the equation are given by x = [-b ± √(b2 - 4ac)]/2a = [-0 ± √(-12)]/2 = ±√(-3) or x = ±1.732i. , The answer is x = ±√(-3) or x = ±1.732i

<s>[INST] [INST] help me answer this question Solve the quadratic equation x2 + 3 = 0, think step by step [/INST]</s> <s>Comparing the given equation with ax2 + bx + c = 0, we have a = 1, b = 0, and c = 3. The discriminant (D) is calculated as D = b2 - 4ac = 02 - 4 × 1 × 3 = -12. Since D < 0, the roots of the equation are given by x = [-b ± √(b2 - 4ac)]/2a = [-0 ± √(-12)]/2 = ±√(-3) or x = ±1.732i. , The answer is x = ±√(-3) or x = ±1.732i</s>

[INST] help me answer this question 7^2 + b^2 = (28/3)^2, think step by step [/INST] , The answer is Squaring both sides of the equation c/a = 4/3, we get a^2 + b^2 = c^2. Substituting the values of a and c, we get 7^2 + b^2 = (28/3)^2.

<s>[INST] [INST] help me answer this question 7^2 + b^2 = (28/3)^2, think step by step [/INST]</s> <s>, The answer is Squaring both sides of the equation c/a = 4/3, we get a^2 + b^2 = c^2. Substituting the values of a and c, we get 7^2 + b^2 = (28/3)^2.</s>

[INST] help me answer this question Describe the sample space for the experiment where two slips are drawn without replacement from a box containing the numbers 1, 2, 3, and 4 on four separate slips., think step by step [/INST] The first event has 4 possible outcomes, and the second event has 3 possible outcomes because 1 slip is already picked. Therefore, the total number of possible outcomes is (4 × 3) = 12. , The answer is The sample space for this experiment includes the following ordered pairs: (1,2), (1,3), (1,4), (2,1), (2,3), (2,4), (3,1), (3,2), (3,4), (4,1), (4,2), (4,3).

<s>[INST] [INST] help me answer this question Describe the sample space for the experiment where two slips are drawn without replacement from a box containing the numbers 1, 2, 3, and 4 on four separate slips., think step by step [/INST]</s> <s>The first event has 4 possible outcomes, and the second event has 3 possible outcomes because 1 slip is already picked. Therefore, the total number of possible outcomes is (4 × 3) = 12. , The answer is The sample space for this experiment includes the following ordered pairs: (1,2), (1,3), (1,4), (2,1), (2,3), (2,4), (3,1), (3,2), (3,4), (4,1), (4,2), (4,3).</s>

[INST] help me answer this question Find the range of the function, think step by step [/INST] , The answer is (i) f(x) = 2 – 3x, x ∈ R, x > 0. Range = (–∞, 2) (ii) f(x) = x2 + 2, x is a real number. Range = [2, ∞) (iii) f(x) = x, x is a real number. Range of f = R

<s>[INST] [INST] help me answer this question Find the range of the function, think step by step [/INST]</s> <s>, The answer is (i) f(x) = 2 – 3x, x ∈ R, x > 0. Range = (–∞, 2) (ii) f(x) = x2 + 2, x is a real number. Range = [2, ∞) (iii) f(x) = x, x is a real number. Range of f = R</s>

[INST] help me answer this question (1 – i) – (–1 + i6), think step by step [/INST] (1 – i) – (–1 + i6) = 1 – i + 1 – i6 = 2 – i7 , The answer is 2 – i7

<s>[INST] [INST] help me answer this question (1 – i) – (–1 + i6), think step by step [/INST]</s> <s>(1 – i) – (–1 + i6) = 1 – i + 1 – i6 = 2 – i7 , The answer is 2 – i7</s>

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

<s>[INST] [INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers except `x = 4`.</s>

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

<s>[INST] [INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers except `x = 4`.</s>

[INST] help me answer this question Simplify the expression: 3x^2 - 2x - 1., think step by step [/INST] , The answer is The simplified expression is (3x - 1)(x + 1).

<s>[INST] [INST] help me answer this question Simplify the expression: 3x^2 - 2x - 1., think step by step [/INST]</s> <s>, The answer is The simplified expression is (3x - 1)(x + 1).</s>

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

<s>[INST] [INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is `x ≥ 1`.</s>

[INST] help me answer this question D ∩ E, think step by step [/INST] , The answer is D ∩ E = (1, 2, 3) ∩ (6) = (φ)

<s>[INST] [INST] help me answer this question D ∩ E, think step by step [/INST]</s> <s>, The answer is D ∩ E = (1, 2, 3) ∩ (6) = (φ)</s>

[INST] help me answer this question Question: If A and G be A.M. and G.M., respectively, between two positive numbers, prove that the numbers are (A + G) / 2 and (A - G) / 2., think step by step [/INST] Explanation: By using the given information on A and G, we can prove that the two numbers are indeed (A + G) / 2 and (A - G) / 2. , The answer is Answer: The numbers are (A + G) / 2 and (A - G) / 2.

<s>[INST] [INST] help me answer this question Question: If A and G be A.M. and G.M., respectively, between two positive numbers, prove that the numbers are (A + G) / 2 and (A - G) / 2., think step by step [/INST]</s> <s>Explanation: By using the given information on A and G, we can prove that the two numbers are indeed (A + G) / 2 and (A - G) / 2. , The answer is Answer: The numbers are (A + G) / 2 and (A - G) / 2.</s>

[INST] help me answer this question Find the domain and the range of the real function f defined by f(x) = √(x - 1)., think step by step [/INST] , The answer is The domain of f is [1, ∞) and its range is [0, ∞).

<s>[INST] [INST] help me answer this question Find the domain and the range of the real function f defined by f(x) = √(x - 1)., think step by step [/INST]</s> <s>, The answer is The domain of f is [1, ∞) and its range is [0, ∞).</s>

[INST] help me answer this question Is number 3 prime?, think step by step [/INST] A prime number is a number that has exactly two distinct positive divisors: 1 and itself. Number 3 has only two distinct positive divisors: 1 and 3. Therefore, 3 is a prime number. , The answer is Yes, number 3 is prime.

<s>[INST] [INST] help me answer this question Is number 3 prime?, think step by step [/INST]</s> <s>A prime number is a number that has exactly two distinct positive divisors: 1 and itself. Number 3 has only two distinct positive divisors: 1 and 3. Therefore, 3 is a prime number. , The answer is Yes, number 3 is prime.</s>

[INST] help me answer this question Find the derivative of (v) x-4 (3 – 4x-5), think step by step [/INST] , The answer is The derivative of x-4 (3 – 4x-5) is not provided.

<s>[INST] [INST] help me answer this question Find the derivative of (v) x-4 (3 – 4x-5), think step by step [/INST]</s> <s>, The answer is The derivative of x-4 (3 – 4x-5) is not provided.</s>

[INST] help me answer this question i9 + i19, think step by step [/INST] i9 + i19 = (i2)4. i + (i2)9. i = (-1)4 . i + (-1)9 .i = 1 x i + -1 x i = i – i = 0 , The answer is 0 + i0

<s>[INST] [INST] help me answer this question i9 + i19, think step by step [/INST]</s> <s>i9 + i19 = (i2)4. i + (i2)9. i = (-1)4 . i + (-1)9 .i = 1 x i + -1 x i = i – i = 0 , The answer is 0 + i0</s>

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

<s>[INST] [INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers except `x = 4`.</s>

[INST] help me answer this question 3(7 + i7) + i(7 + i7) = 14 + i28, think step by step [/INST] Expanding the left side, we get 21 + 3i7 + 7i - i9 = 21 + i8 - i9 = 2 - i1 + 7i = 2 + 6i = 2 - i7 , The answer is 2 – i7

<s>[INST] [INST] help me answer this question 3(7 + i7) + i(7 + i7) = 14 + i28, think step by step [/INST]</s> <s>Expanding the left side, we get 21 + 3i7 + 7i - i9 = 21 + i8 - i9 = 2 - i1 + 7i = 2 + 6i = 2 - i7 , The answer is 2 – i7</s>

[INST] help me answer this question Find the slope of the line CA., think step by step [/INST] , The answer is The slope of the line CA (m3) = (4+1)/(4+1) = 5/5 = 1

<s>[INST] [INST] help me answer this question Find the slope of the line CA., think step by step [/INST]</s> <s>, The answer is The slope of the line CA (m3) = (4+1)/(4+1) = 5/5 = 1</s>

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

<s>[INST] [INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers except `x = 4`.</s>

[INST] help me answer this question Find an+1/an, for n = 1, 2, 3, 4, 5 in the Fibonacci sequence defined by 1 = a1 = a2 and an = an-1 + an-2, n > 2, think step by step [/INST] Given, 1 = a1 = a2 and an = an-1 + an-2, n > 2. Then, a3/a2 = 2/1 = 1, a4/a3 = 3/2, a5/a4 = 5/3, a6/a5 = 8/5. , The answer is a3/a2 = 1, a4/a3 = 3/2, a5/a4 = 2, a6/a5 = 5/3

<s>[INST] [INST] help me answer this question Find an+1/an, for n = 1, 2, 3, 4, 5 in the Fibonacci sequence defined by 1 = a1 = a2 and an = an-1 + an-2, n > 2, think step by step [/INST]</s> <s>Given, 1 = a1 = a2 and an = an-1 + an-2, n > 2. Then, a3/a2 = 2/1 = 1, a4/a3 = 3/2, a5/a4 = 5/3, a6/a5 = 8/5. , The answer is a3/a2 = 1, a4/a3 = 3/2, a5/a4 = 2, a6/a5 = 5/3</s>

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

<s>[INST] [INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is `x ≥ 1`.</s>

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

<s>[INST] [INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers.</s>

[INST] help me answer this question Select a point (0, 0)., think step by step [/INST] The solution region of the given inequality is below the line 3x + 4y = 12. (That is, the origin is included in the region.) , The answer is 3 × (0) + 4 × (0) ≤ 12

<s>[INST] [INST] help me answer this question Select a point (0, 0)., think step by step [/INST]</s> <s>The solution region of the given inequality is below the line 3x + 4y = 12. (That is, the origin is included in the region.) , The answer is 3 × (0) + 4 × (0) ≤ 12</s>

[INST] help me answer this question Let us make the table of the given data and append other columns after calculations., think step by step [/INST] Here, the user is required to make a table of given data and add other columns after performing some calculations. , The answer is In this question, the user is being asked to create a table of the given data and append other columns after calculations.

<s>[INST] [INST] help me answer this question Let us make the table of the given data and append other columns after calculations., think step by step [/INST]</s> <s>Here, the user is required to make a table of given data and add other columns after performing some calculations. , The answer is In this question, the user is being asked to create a table of the given data and append other columns after calculations.</s>

[INST] help me answer this question Find the equation of the line intersecting the y-axis at a distance of 2 units above the origin and making an angle of 30o with positive direction of the x-axis., think step by step [/INST] , The answer is The equation of the line is x – √3 y + 2√3 = 0.

<s>[INST] [INST] help me answer this question Find the equation of the line intersecting the y-axis at a distance of 2 units above the origin and making an angle of 30o with positive direction of the x-axis., think step by step [/INST]</s> <s>, The answer is The equation of the line is x – √3 y + 2√3 = 0.</s>

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

<s>[INST] [INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is `x ≥ 1`.</s>

[INST] help me answer this question Find the 15th term of the arithmetic sequence., think step by step [/INST] The nth term of the arithmetic sequence is given by an = n + 10. To find the 15th term, substitute n = 15 into the formula to get a15 = 15 + 10 = 24. , The answer is The 15th term is 24.

<s>[INST] [INST] help me answer this question Find the 15th term of the arithmetic sequence., think step by step [/INST]</s> <s>The nth term of the arithmetic sequence is given by an = n + 10. To find the 15th term, substitute n = 15 into the formula to get a15 = 15 + 10 = 24. , The answer is The 15th term is 24.</s>

[INST] help me answer this question Prove that cos2 2x – cos2 6x = sin 4x sin 8x, think step by step [/INST] Using sum and difference formulas, cos 6x can be written as cos (2x + 4x) and cos 4x can be written as cos (2x + 2x). Then applying the formula for cos (a + b) and cos (a - b) and using some trigonometric identities, the result can be obtained. , The answer is cos2 2x – cos2 6x = sin 4x sin 8x

<s>[INST] [INST] help me answer this question Prove that cos2 2x – cos2 6x = sin 4x sin 8x, think step by step [/INST]</s> <s>Using sum and difference formulas, cos 6x can be written as cos (2x + 4x) and cos 4x can be written as cos (2x + 2x). Then applying the formula for cos (a + b) and cos (a - b) and using some trigonometric identities, the result can be obtained. , The answer is cos2 2x – cos2 6x = sin 4x sin 8x</s>

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

<s>[INST] [INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers except `x = 4`.</s>

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

<s>[INST] [INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers except `x = 4`.</s>

[INST] help me answer this question Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by R = {(a, b): a, b ∈ A, b is exactly divisible by a}. Write R in roster form. Find the domain of R and the range of R. , think step by step [/INST] , The answer is R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (6, 6)}

<s>[INST] [INST] help me answer this question Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by R = {(a, b): a, b ∈ A, b is exactly divisible by a}. Write R in roster form. Find the domain of R and the range of R. , think step by step [/INST]</s> <s>, The answer is R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (6, 6)}</s>

[INST] help me answer this question (iv) Only subset of Φ is Φ., think step by step [/INST] , The answer is N/A

<s>[INST] [INST] help me answer this question (iv) Only subset of Φ is Φ., think step by step [/INST]</s> <s>, The answer is N/A</s>

[INST] help me answer this question Find the equation of the circle with the given condition: 144x2 – 144x + 36y2 – 72y + 36 + 144y2 – 72y + 9 – 1 = 0, think step by step [/INST] , The answer is The equation of the circle is 36x2 + 36y2 – 36x – 18y + 44 = 0

<s>[INST] [INST] help me answer this question Find the equation of the circle with the given condition: 144x2 – 144x + 36y2 – 72y + 36 + 144y2 – 72y + 9 – 1 = 0, think step by step [/INST]</s> <s>, The answer is The equation of the circle is 36x2 + 36y2 – 36x – 18y + 44 = 0</s>

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

<s>[INST] [INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers.</s>

[INST] help me answer this question Solve 5x – 3 < 7. , think step by step [/INST] N/A , The answer is The solution set is {…, -2, -1, 0, 1}.

<s>[INST] [INST] help me answer this question Solve 5x – 3 < 7. , think step by step [/INST]</s> <s>N/A , The answer is The solution set is {…, -2, -1, 0, 1}.</s>

[INST] help me answer this question Given x2/49 + y2/36 = 1, what is the eccentricity?, think step by step [/INST] , The answer is Eccentricity, e = c/a = √13/7

<s>[INST] [INST] help me answer this question Given x2/49 + y2/36 = 1, what is the eccentricity?, think step by step [/INST]</s> <s>, The answer is Eccentricity, e = c/a = √13/7</s>

[INST] help me answer this question We can write the given statement as P(n): (2n +7) < (n + 3)2. Is it true for n=1?, think step by step [/INST] , The answer is Yes, it is true. For n=1, we get 2.1 + 7 = 9 < (1 + 3)2 = 16.

<s>[INST] [INST] help me answer this question We can write the given statement as P(n): (2n +7) < (n + 3)2. Is it true for n=1?, think step by step [/INST]</s> <s>, The answer is Yes, it is true. For n=1, we get 2.1 + 7 = 9 < (1 + 3)2 = 16.</s>

[INST] help me answer this question (a + 8) (a – 2) = 0, think step by step [/INST] , The answer is Factoring the quadratic equation a^2 + 8a – 2a – 16 = 0, we get (a + 8) (a – 2) = 0.

<s>[INST] [INST] help me answer this question (a + 8) (a – 2) = 0, think step by step [/INST]</s> <s>, The answer is Factoring the quadratic equation a^2 + 8a – 2a – 16 = 0, we get (a + 8) (a – 2) = 0.</s>

[INST] help me answer this question Prove that (sin 3x + sin x) sin x + (cos 3x – cos x) cos x = 0, think step by step [/INST] This involves the use of trigonometric formulas and simplification. , The answer is LHS = sin 3x sin x + sin^2 x + cos 3x cos x – cos^2 x = cos 2x – cos^2 x = 0 = RHS

<s>[INST] [INST] help me answer this question Prove that (sin 3x + sin x) sin x + (cos 3x – cos x) cos x = 0, think step by step [/INST]</s> <s>This involves the use of trigonometric formulas and simplification. , The answer is LHS = sin 3x sin x + sin^2 x + cos 3x cos x – cos^2 x = cos 2x – cos^2 x = 0 = RHS</s>

[INST] help me answer this question Write the decimal equivalent of the fraction 3/4., think step by step [/INST] To convert the fraction 3/4 to a decimal, you would divide 3 by 4. , The answer is The decimal equivalent of the fraction 3/4 is 0.75.

<s>[INST] [INST] help me answer this question Write the decimal equivalent of the fraction 3/4., think step by step [/INST]</s> <s>To convert the fraction 3/4 to a decimal, you would divide 3 by 4. , The answer is The decimal equivalent of the fraction 3/4 is 0.75.</s>

[INST] help me answer this question Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that (i) A × (B ∩ C) = (A × B) ∩ (A × C) (ii) A × C is a subset of B × D, think step by step [/INST] , The answer is i) Both L.H.S. and R.H.S. are equal to Φ, hence verified. ii) Since all the elements of set A × C are the elements of set B × D, therefore A × C is a subset of B × D.

<s>[INST] [INST] help me answer this question Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that (i) A × (B ∩ C) = (A × B) ∩ (A × C) (ii) A × C is a subset of B × D, think step by step [/INST]</s> <s>, The answer is i) Both L.H.S. and R.H.S. are equal to Φ, hence verified. ii) Since all the elements of set A × C are the elements of set B × D, therefore A × C is a subset of B × D.</s>

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

<s>[INST] [INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is `x ≥ 1`.</s>

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

<s>[INST] [INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers except `x = 4`.</s>

[INST] help me answer this question Find the number of litres that the owner of a milk store could sell weekly at Rs. 17/litre., think step by step [/INST] , The answer is The owner can sell 1340 litres weekly at Rs. 17/litre.

<s>[INST] [INST] help me answer this question Find the number of litres that the owner of a milk store could sell weekly at Rs. 17/litre., think step by step [/INST]</s> <s>, The answer is The owner can sell 1340 litres weekly at Rs. 17/litre.</s>

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

<s>[INST] [INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers except `x = 4`.</s>

[INST] help me answer this question Are all integers negative?, think step by step [/INST] An integer is a whole number, positive or negative, or zero. Therefore, not all integers are negative, because there are also positive integers and zero. , The answer is No, not all integers are negative.

<s>[INST] [INST] help me answer this question Are all integers negative?, think step by step [/INST]</s> <s>An integer is a whole number, positive or negative, or zero. Therefore, not all integers are negative, because there are also positive integers and zero. , The answer is No, not all integers are negative.</s>

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

<s>[INST] [INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers except `x = 4`.</s>

[INST] help me answer this question Find r if (i)5Pr = 26Pr-1 (ii) 5Pr = 6Pr-1, think step by step [/INST] We can solve these equations by using the formula of nPr. , The answer is { (i) r = 6, (ii) r = 5 }

<s>[INST] [INST] help me answer this question Find r if (i)5Pr = 26Pr-1 (ii) 5Pr = 6Pr-1, think step by step [/INST]</s> <s>We can solve these equations by using the formula of nPr. , The answer is { (i) r = 6, (ii) r = 5 }</s>

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

<s>[INST] [INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers.</s>

[INST] help me answer this question Evaluate (x + 1)6 + (x - 1)6. Hence, or otherwise, evaluate (√2 + 1)6 + (√2 - 1)6., think step by step [/INST] The binomial theorem is used to express the given expressions and then the values of x are substituted. , The answer is 198

<s>[INST] [INST] help me answer this question Evaluate (x + 1)6 + (x - 1)6. Hence, or otherwise, evaluate (√2 + 1)6 + (√2 - 1)6., think step by step [/INST]</s> <s>The binomial theorem is used to express the given expressions and then the values of x are substituted. , The answer is 198</s>

[INST] help me answer this question Here, the elements of this set are natural numbers as well as divisors of 6. Hence, (i) matches with (c)., think step by step [/INST] , The answer is The elements of set (i) are natural numbers and divisors of 6, which makes it match with set (c).

<s>[INST] [INST] help me answer this question Here, the elements of this set are natural numbers as well as divisors of 6. Hence, (i) matches with (c)., think step by step [/INST]</s> <s>, The answer is The elements of set (i) are natural numbers and divisors of 6, which makes it match with set (c).</s>

[INST] help me answer this question (vi) {1, 2, 5} ⊂ A is correct, think step by step [/INST] , The answer is Each element of {1, 2, 5} is also an element of A.

<s>[INST] [INST] help me answer this question (vi) {1, 2, 5} ⊂ A is correct, think step by step [/INST]</s> <s>, The answer is Each element of {1, 2, 5} is also an element of A.</s>

[INST] help me answer this question FI, think step by step [/INST] I is not defined in the question. , The answer is FI = Not provided

<s>[INST] [INST] help me answer this question FI, think step by step [/INST]</s> <s>I is not defined in the question. , The answer is FI = Not provided</s>

[INST] help me answer this question The relation f is defined by f = {(x, y): y = x^2, 0 ≤ x < 3} and g is defined by g = {(x, y): y = x, 1 ≤ x ≤ 4}. Show that f is a function and g is not a function., think step by step [/INST] A relation is a function if for every value of x in its domain, there is only one value of y. In this case, f satisfies this property and hence is a function, while g does not and hence is not a function. , The answer is The relation f is a function as for every value of x in the given domain (0 ≤ x < 3), there is only one value of y such that (x, y) belongs to f. However, the relation g is not a function as for x = 2, there are two values of y (2 and 3) such that (x, y) belongs to g.

<s>[INST] [INST] help me answer this question The relation f is defined by f = {(x, y): y = x^2, 0 ≤ x < 3} and g is defined by g = {(x, y): y = x, 1 ≤ x ≤ 4}. Show that f is a function and g is not a function., think step by step [/INST]</s> <s>A relation is a function if for every value of x in its domain, there is only one value of y. In this case, f satisfies this property and hence is a function, while g does not and hence is not a function. , The answer is The relation f is a function as for every value of x in the given domain (0 ≤ x < 3), there is only one value of y such that (x, y) belongs to f. However, the relation g is not a function as for x = 2, there are two values of y (2 and 3) such that (x, y) belongs to g.</s>

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

<s>[INST] [INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is `x ≥ 1`.</s>

[INST] help me answer this question (viii) {x: x + 5 = 8}, think step by step [/INST] , The answer is {x: x ∈ N and x ≠ 3}

<s>[INST] [INST] help me answer this question (viii) {x: x + 5 = 8}, think step by step [/INST]</s> <s>, The answer is {x: x ∈ N and x ≠ 3}</s>

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

<s>[INST] [INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST]</s> <s>, The answer is The domain of the function is all real numbers.</s>