messages listlengths 1 1 | ground_truth stringclasses 22 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (2(-3e^(-1(1(-5x) - 1)) + 1) - 1)/(-2(-3e^(-1(1(-5x) - 1)) + 1) + 3) and g(x) = 1|(-2|(-3x - 1) + 2| + 2) - 1| - 1 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex... | 0 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 1(5(3|(-4x - 5) + 3| - 2)^2 - 3(3|(-4x - 5) + 3| - 2) + 5) + 4 and g(x) = -4(-3|(1cos(2πx + 1) + 3) - 2| + 2) + 5 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex ... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3((3((2(4x^2 - 4x - 4))/(3(4x^2 - 4x - 4) - 2)) + 1)/(3((2(4x^2 - 4x - 4))/(3(4x^2 - 4x - 4) - 2)) - 2))^2 + 5((3((2(4x^2 - 4x - 4))/(3(4x^2 - 4x - 4) - 2)) + 1)/(3((2(4x^2 - 4x - 4))/(3(4x^2 - 4x - 4) - 2)) - 2)) +... | 2 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 3(-1(-2(-4x - 2) - 4) + 4) - 2 and g(x) = -2sin(2π(-1(-2x^2 - 4x - 5) + 3) + 2) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = (-3(-3(5((2x + 3)/(1x)) - 4) - 1) - 3)/(2(-3(5((2x + 3)/(1x)) - 4) - 1) + 1) and g(x) = -1(2cos(2π((2x - 1)/(-2x + 3)) + 1)) - 5 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | -2 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -4((1(-3(-1x^2 + 5x - 1) + 2) + 2)/(-2(-3(-1x^2 + 5x - 1) + 2) - 3)) - 3 and g(x) = -3|(-1cos(2π(1x^2 - 3x - 5) + 3) + 3) + 1| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your ... | 5 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1|(-2|((3((3x + 1)/(-1x + 2)))/(1((3x + 1)/(-1x + 2)) + 3)) - 3| + 2) - 3| + 3 and g(x) = -1(-1(-1|x| - 3) - 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 6 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 3(2(1(2x^2 - 5x + 1) - 3)^2 - 3(1(2x^2 - 5x + 1) - 3) + 4)^2 - 5(2(1(2x^2 - 5x + 1) - 3)^2 - 3(1(2x^2 - 5x + 1) - 3) + 4) + 1 and g(x) = -2(-1(-2sin(2πx - 2) - 3)^2 + 1(-2sin(2πx - 2) - 3)) + 2 meet in the interval [-10, 10] and round ... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (1((3((-2(-1x^2 + 2x))/(-2(-1x^2 + 2x) - 1)) - 1)/(-1((-2(-1x^2 + 2x))/(-2(-1x^2 + 2x) - 1)) - 1)) + 2)/(-1((3((-2(-1x^2 + 2x))/(-2(-1x^2 + 2x) - 1)) - 1)/(-1((-2(-1x^2 + 2x))/(-2(-1x^2 + 2x) - 1)) - 1)) + 2) and g(x) = 2... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -2(-2((1(-1sin(3πx + 1) + 3) + 1)/(-1(-1sin(3πx + 1) + 3) - 3)) - 1)^2 - 3 and g(x) = 5((1(-1x^2 - 5x - 5) - 1)/(2(-1x^2 - 5x - 5) - 1)) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\bo... | -3 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (2(1|((3((-3x + 2)/(-2x)) + 2)/(-2((-3x + 2)/(-2x)) - 3)) + 1| + 1))/(2(1|((3((-3x + 2)/(-2x)) + 2)/(-2((-3x + 2)/(-2x)) - 3)) + 1| + 1) - 3) and g(x) = 2|(4(1x^2 + 3x - 5)^2 - 4(1x^2 + 3x - 5) - 2) - 2| - 1 intersect in... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1e^(-1(-1|(-1((-1x + 3)/(-2x + 1)) - 4) + 1| + 2)) - 2 and g(x) = -1(2((3x - 2)/(-1x + 3)) - 1)^2 + 2(2((3x - 2)/(-1x + 3)) - 1) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Yo... | 1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -1|(-2e^(-1(-3|((3x - 2)/(3x + 1)) + 1| + 3)) + 1) - 3| - 2 and g(x) = -1e^(-2(-2(-5x) + 4)) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (-3(3e^(-1((-3((3x - 3)/(-3x)) + 2)/(2((3x - 3)/(-3x)) - 1))) + 1) + 1)/(1(3e^(-1((-3((3x - 3)/(-3x)) + 2)/(2((3x - 3)/(-3x)) - 1))) + 1) + 1) and g(x) = -1(1(1x^2 + 5) - 5) + 4 meet in the interval [-10, 10] and round to the nearest i... | 0 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 5(-1((-2(-1x + 2) - 3)/(-1(-1x + 2) + 3)) - 4) - 4 and g(x) = -4((1((-1x - 1)/(1x)) - 2)/(-3((-1x - 1)/(1x))))^2 - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex for... | -1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -4(2|(2e^(-1(-1|x + 1| - 1)) + 3) - 2| - 1)^2 - 4 and g(x) = -4(3|((2x + 3)/(2x + 1)) + 2| - 1)^2 + 4(3|((2x + 3)/(2x + 1)) + 2| - 1) + 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your a... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (3((3(5(-1|x - 1|)) - 2)/(2(5(-1|x - 1|)) + 2)) + 2)/(2((3(5(-1|x - 1|)) - 2)/(2(5(-1|x - 1|)) + 2)) + 1) and g(x) = 3|((-1(1e^(-1x) - 1) - 2)/(-2(1e^(-1x) - 1) - 1))| - 2 intersect in the interval [-10, 10]?\n\nPresent ... | 3 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 3(3(-2((-2x - 3)/(-3x - 1)) - 3) + 4) + 1 and g(x) = 3cos(2π(2|(-4x^2 - 5x - 2) + 3| - 3) + 1) + 1 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 5(-1|(5(-4x + 5) + 1) - 1| + 3)^2 - 3(-1|(5(-4x + 5) + 1) - 1| + 3) - 5 and g(x) = 1(-2(-3e^(-1x) - 3) + 5)^2 + 1(-2(-3e^(-1x) - 3) + 5) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\bo... | -3 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1(2(1(-3x + 2) + 2) - 2)^2 and g(x) = -1(-2|(-1x)| - 3)^2 + 2(-2|(-1x)| - 3) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 1sin(1π((-2(-1|(3|x + 1| + 1) - 3| - 2) + 1)/(1(-1|(3|x + 1| + 1) - 3| - 2))) - 3) - 3 and g(x) = (-1(1|(1e^(1x) - 2) - 1| - 2) + 1)/(-1(1|(1e^(1x) - 2) - 1| - 2) - 2) meet in the interval [-10,... | 1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 3((-1((1(-3e^(1x) + 3) - 1)/(2(-3e^(1x) + 3))) - 1)/(-1((1(-3e^(1x) + 3) - 1)/(2(-3e^(1x) + 3))) + 3)) + 2 and g(x) = -1|(2sin(3π((3x)/(-3x + 1)) + 1) - 2) + 1| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \... | 0 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (2(2(1|(-1|x + 2|) - 3| - 2)^2 + 3(1|(-1|x + 2|) - 3| - 2) + 5) - 1)/(-1(2(1|(-1|x + 2|) - 3| - 2)^2 + 3(1|(-1|x + 2|) - 3| - 2) + 5) + 3) and g(x) = 3(-1(2x - 3) - 3)^2 + 2(-1(2x - 3) - 3... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 1e^(-2(-2(-4((-2x + 3)/(2x - 1))^2 - 3((-2x + 3)/(2x - 1)) - 5) + 3)) + 1 and g(x) = 3((1(-5x - 5) + 1)/(-2(-5x - 5) - 3)) - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answe... | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = (1(-1(-3(-3|x + 2| + 1)^2 + 1(-3|x + 2| + 1) - 4) - 3) - 2)/(1(-1(-3(-3|x + 2| + 1)^2 + 1(-3|x + 2| + 1) - 4) - 3) + 3) and g(x) = -1(-4(1x - 3) + 3) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your... | 5 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (-3(-1(-1(-3e^(-2x) - 3)^2 + 2(-3e^(-2x) - 3))^2 - 4(-1(-3e^(-2x) - 3)^2 + 2(-3e^(-2x) - 3)) - 3) - 2)/(2(-1(-1(-3e^(-2x) - 3)^2 + 2(-3e^(-2x) - 3))^2 - 4(-1(-3e^(-2x) - 3)^2 + 2(-3e^(-2x) - 3)) - 3) + 1) and g(x) = 1(-4(-3|x + 1| + 1)... | -2 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 2(2(1(2|x| + 3) - 4) + 4)^2 + 4(2(1(2|x| + 3) - 4) + 4) + 1 and g(x) = 2|(3(3|x + 1| + 2) + 4) + 3| - 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 1|(3(1|(1|x - 1| - 3) + 3| - 1)) - 3| + 3 and g(x) = 3|(2e^(-1(1x - 4)) - 1) + 3| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1(1(-4((3x + 1)/(2x + 3)) - 3) - 5)^2 + 5(1(-4((3x + 1)/(2x + 3)) - 3) - 5) - 3 and g(x) = -1sin(3π(5(3|x + 2| + 3) + 1) + 2) - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex ... | -1 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -2|(-5(-2|(2sin(3πx + 3) - 2) - 2| - 3) - 2) + 2| + 1 and g(x) = -3(-1(-3e^(-2x) + 2) + 1)^2 + 2(-1(-3e^(-2x) + 2) + 1) - 4 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | -1 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 4(-4(-4(-2x^2 - 5x - 2) + 1) + 2) + 4 and g(x) = (-2(2cos(1π(-4x - 5) + 2) - 3))/(-1(2cos(1π(-4x - 5) + 2) - 3) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex fo... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 3|(-2sin(1π((-3(5x^2 + 1x + 4) - 1)/(-1(5x^2 + 1x + 4) - 1)) + 2)) - 2| and g(x) = -1(-3(-2|x - 2| + 1) + 1) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 2 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 1(1(-1((-3x + 1)/(3x - 2))^2 + 3((-3x + 1)/(3x - 2))) - 1)^2 + 5(1(-1((-3x + 1)/(3x - 2))^2 + 3((-3x + 1)/(3x - 2))) - 1) + 2 and g(x) = 4(-3(-1x + 1) + 4)^2 + 5(-3(-1x + 1) + 4) + 1 meet in the interval [-10, 10].\n\nPres... | 1 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -2((-1(-1((-1x - 1)/(-3x - 1)) - 1) + 3)/(-2(-1((-1x - 1)/(-3x - 1)) - 1) + 3))^2 - 3((-1(-1((-1x - 1)/(-3x - 1)) - 1) + 3)/(-2(-1((-1x - 1)/(-3x - 1)) - 1) + 3)) - 1 and g(x) = (-1(2|(2|... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -1((2((-1(4x^2 + 3x) - 2)/(3(4x^2 + 3x) - 1)) + 3)/(2((-1(4x^2 + 3x) - 2)/(3(4x^2 + 3x) - 1)) - 3)) - 5 and g(x) = -2(3|((3x + 1)/(3x - 2)) + 2| + 2)^2 + 5(3|((3x + 1)/(3x - 2)) + 2| + 2) - 2 meet in the interval [-10, 10] and round to... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2(-1|(-3((2x + 3)/(1x + 3)) + 5) - 2| - 3) and g(x) = (-2(4(3e^(1x) - 1) - 1))/(-3(4(3e^(1x) - 1) - 1) + 4) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | -1 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 3((-3(-1sin(1π((-3x)/(1x + 1)) - 3) + 3) - 1)/(-1(-1sin(1π((-3x)/(1x + 1)) - 3) + 3)))^2 + 4((-3(-1sin(1π((-3x)/(1x + 1)) - 3) + 3) - 1)/(-1(-1sin(1π((-3x)/(1x + 1)) - 3) + 3))) + 3 and g(x) = (3(-2((-1x)/(-1x + 3)) - 3))/(-3(-2((-1x)... | 2 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (2(-2|(-1cos(3π(-5x + 3)) - 1) + 3| - 3) - 3)/(-3(-2|(-1cos(3π(-5x + 3)) - 1) + 3| - 3) + 4) and g(x) = (-1(2|(3x - 4) - 2| - 3) + 2)/(-2(2|(3x - 4) - 2| - 3)) meet in the interval [-10, 10] and round to the nearest integer, what do yo... | 4 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -5((-3(1((3x - 3)/(3x - 1))^2 + 1((3x - 3)/(3x - 1)) - 4) + 3)/(3(1((3x - 3)/(3x - 1))^2 + 1((3x - 3)/(3x - 1)) - 4) - 2)) - 3 and g(x) = -4((-1(1cos(2πx + 2) - 3) + 3)/(-1(1cos(2πx + 2) - 3) - 2))^2 + 1((-1(1cos(2πx + 2) - 3) + 3)/(-1(1cos(2... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2|((2(-2|((3x)/(2x + 3)) + 3| - 2) + 2)/(-3(-2|((3x)/(2x + 3)) + 3| - 2) + 4)) + 3| and g(x) = (1(1(-3x + 4)) - 3)/(3(1(-3x + 4)) + 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Y... | 1 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1((-3(3e^(2(2|x + 3| - 3)) + 2) + 3)/(1(3e^(2(2|x + 3| - 3)) + 2) + 1))^2 + 4((-3(3e^(2(2|x + 3| - 3)) + 2) + 3)/(1(3e^(2(2|x + 3| - 3)) + 2) + 1)) - 2 and g(x) = (2(-1|(2e^(-1x) - 1) - 3| + 1) + 3)/(-1(-1|(2e^(-1x... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (1((-1((-1(-1sin(3πx) + 1) + 1)/(-1(-1sin(3πx) + 1) + 2)))/(1((-1(-1sin(3πx) + 1) + 1)/(-1(-1sin(3πx) + 1) + 2)) + 3)))/(-2((-1((-1(-1sin(3πx) + 1) + 1)/(-1(-1sin(3πx) + 1) + 2)))/(1((-1(-1sin(3πx) + 1) + 1)/(-1(-1sin(3πx... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (-3(1|(1cos(3π((-2x - 3)/(-1x + 3)))) + 2| + 1) + 2)/(2(1|(1cos(3π((-2x - 3)/(-1x + 3)))) + 2| + 1) - 3) and g(x) = 4(-2(-1e^(-1x) + 1)^2 + 2(-1e^(-1x) + 1) + 1)^2 - 5(-2(-1e^(-1x) + 1)^2 + 2(-1e^(-1x) + 1) + 1) - 1 meet in... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (1(-1(3e^(-1(-1|x + 1| + 1)) + 1)^2 - 2(3e^(-1(-1|x + 1| + 1)) + 1) - 1) - 1)/(-2(-1(3e^(-1(-1|x + 1| + 1)) + 1)^2 - 2(3e^(-1(-1|x + 1| + 1)) + 1) - 1)) and g(x) = 2(1((2x + 3)/(-1x - 1)) - 1) - 3 meet in the interva... | -1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (2((3(2sin(1π(-2x^2 - 1x + 2) - 2) + 1) - 2)/(-3(2sin(1π(-2x^2 - 1x + 2) - 2) + 1) - 3)) - 1)/(3((3(2sin(1π(-2x^2 - 1x + 2) - 2) + 1) - 2)/(-3(2sin(1π(-2x^2 - 1x + 2) - 2) + 1) - 3)) - 1) and g(x) = 4(3((... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 5((1(-4(4x^2 - 2x) + 5) + 3)/(-1(-4(4x^2 - 2x) + 5) + 2)) + 2 and g(x) = -5(1|(1e^(-2x) - 3) - 2| - 3)^2 - 3(1|(1e^(-2x) - 3) - 2| - 3) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\box... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (1((3((1(4x - 1) - 3)/(2(4x - 1) - 3)) - 1)/(-3((1(4x - 1) - 3)/(2(4x - 1) - 3)) - 2)) - 3)/(-3((3((1(4x - 1) - 3)/(2(4x - 1) - 3)) - 1)/(-3((1(4x - 1) - 3)/(2(4x - 1) - 3)) - 2)) + 2) and g(x) = 2|(2e^(-1(-2x + 3)) ... | 1 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 1|(-3(1(5x^2 + 2x + 5)^2 - 4(5x^2 + 2x + 5) - 3)^2 + 3(1(5x^2 + 2x + 5)^2 - 4(5x^2 + 2x + 5) - 3) + 1) + 1| + 2 and g(x) = 3|(1(-1e^(1x) + 3)^2 + 5(-1e^(1x) + 3) + 1) - 2| - 1 intersect in... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (2((1((-1(-2|x + 2| - 1) - 3)/(2(-2|x + 2| - 1))) + 2)/(1((-1(-2|x + 2| - 1) - 3)/(2(-2|x + 2| - 1))) + 3)) + 2)/(-2((1((-1(-2|x + 2| - 1) - 3)/(2(-2|x + 2| - 1))) + 2)/(1((-1(-2|x + 2| - 1) - 3)/(2(-2|x + 2| - 1))) ... | 7 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (1(2((-1(-2x^2 + 5x - 5) - 3)/(2(-2x^2 + 5x - 5) + 3)) - 3) + 3)/(1(2((-1(-2x^2 + 5x - 5) - 3)/(2(-2x^2 + 5x - 5) + 3)) - 3)) and g(x) = (-1((-2((2x - 2)/(-2x - 2)) - 3)/(-2((2x - 2)/(-2x - 2)) - 1)) + 2)/(2((-2((2x - 2)... | 2 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -2|(1(-2|(3cos(2πx - 2)) - 1| + 2)) - 1| - 3 and g(x) = (-2(1(-2|x - 1| + 1)^2 - 5(-2|x - 1| + 1) + 3) - 2)/(-1(1(-2|x - 1| + 1)^2 - 5(-2|x - 1| + 1) + 3)) meet in the interval [-10, 10]?\n\nPre... | 1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 1e^(-1(1(-3|((2x)/(2x - 1)) - 1| + 2) + 3)) and g(x) = 1(-3(-1x - 3)^2 - 3(-1x - 3) - 5)^2 - 1(-3(-1x - 3)^2 - 3(-1x - 3) - 5) - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex ... | 0 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 2(-1sin(1π((2(4x^2 - 1x - 5) + 3)/(-2(4x^2 - 1x - 5) + 1)) + 1) + 2)^2 + 2(-1sin(1π((2(4x^2 - 1x - 5) + 3)/(-2(4x^2 - 1x - 5) + 1)) + 1) + 2) + 1 and g(x) = (3((-1(-2x + 3) + 1)/(2(-2x + 3) + 1)) + 3)/(-2((-1(-2x + 3) + 1)/(2(-2x + 3)... | 2 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 4(-2|(-1(-1sin(1πx + 2) + 3)^2 + 4(-1sin(1πx + 2) + 3) - 2) + 3| - 1)^2 + 3 and g(x) = 1(-5(-3|x| + 2) - 4)^2 - 5(-5(-3|x| + 2) - 4) - 4 meet in the interval [-10, 10]?\n\nPresent the answer in ... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 2((-3((3((2x + 2)/(-1x + 3)) - 1)/(2((2x + 2)/(-1x + 3)) - 3)))/(-3((3((2x + 2)/(-1x + 3)) - 1)/(2((2x + 2)/(-1x + 3)) - 3)) - 1))^2 + 2((-3((3((2x + 2)/(-1x + 3)) - 1)/(2((2x + 2)/(-1x + 3)) - 3)))/(-3((3((2x + 2)/(-1x + 3)) - 1)/(2((... | -4 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 1(-2(1(1|x + 2|)^2 - 4(1|x + 2|)) + 4) + 1 and g(x) = 4(5(-3x + 5) - 4)^2 + 2(5(-3x + 5) - 4) - 4 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{... | 2 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 1|(3(3(1e^(-1x)) + 1) + 2) + 2| - 2 and g(x) = (2(3|(4x + 2) - 2| - 2) + 1)/(-1(3|(4x + 2) - 2| - 2)) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Y... | 0 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -1(4(-3((1x + 3)/(-1x - 1)) - 5)^2 - 1(-3((1x + 3)/(-1x - 1)) - 5) + 4)^2 - 5(4(-3((1x + 3)/(-1x - 1)) - 5)^2 - 1(-3((1x + 3)/(-1x - 1)) - 5) + 4) + 5 and g(x) = (1(-1|(4x^2 - 5x + 5) - 3| + 2) - 3)/(-1(-1|(4x^2 - 5x + 5) - 3| + 2)) i... | 1 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 1e^(-1(-1(-1|(-3x + 4) + 1| + 3)^2 - 5(-1|(-3x + 4) + 1| + 3) - 4)) + 1 and g(x) = (-1(3|(3e^(-1x) - 1) - 2| - 2) + 3)/(1(3|(3e^(-1x) - 1) - 2| - 2) + 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex forma... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = (-1(1(-5((-2x + 1)/(3x))^2 - 1((-2x + 1)/(3x)) + 2) + 5) + 1)/(2(1(-5((-2x + 1)/(3x))^2 - 1((-2x + 1)/(3x)) + 2) + 5) - 3) and g(x) = -1|(2|(3e^(1x) + 1) - 3| - 1) + 1| - 1 meet in the interval [-10, 10].\n\nPresent the an... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 2|(2|(-3|(2|x + 2| - 2) + 2| - 3) - 1| - 2) + 3| + 3 and g(x) = (-2((-1((-3x - 3)/(-1x - 3)) + 3)/(2((-3x - 3)/(-1x - 3)) - 3)) - 2)/(3((-1((-3x - 3)/(-1x - 3)) + 3)/(2((-3x - 3)/(-1x - 3)) - 3)) + 2) meet in the int... | -2 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 3(-4(5(1x)^2 + 1(1x))^2 + 5(5(1x)^2 + 1(1x)) + 4) - 3 and g(x) = -1|(-4(4x^2 - 3x) - 4) + 2| + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -1|(-5(-1sin(1π(2x - 1) - 2) + 1) + 5) + 1| - 2 and g(x) = (-1(-5(3x^2 - 1x - 4) + 1))/(-1(-5(3x^2 - 1x - 4) + 1) - 2) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | -1 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 1|(-2cos(2π((2(3x^2 + 2x + 5) - 3)/(1(3x^2 + 2x + 5))) - 1) + 1) - 1| - 3 and g(x) = -5(1(2|x - 3|)) - 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Y... | 6 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 3(1((3((1x)/(2x + 1)) - 2)/(-2((1x)/(2x + 1)) - 2)) - 1) + 2 and g(x) = 2|((-3(2cos(1πx - 3) + 3) - 2)/(-1(2cos(1πx - 3) + 3) - 1)) - 3| + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -2e^(2(-3|(-1((1x - 2)/(2x - 1))^2 - 3((1x - 2)/(2x - 1)) + 3) - 2| - 3)) + 3 and g(x) = 1(-3|(2x + 5) + 2| + 3) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -3 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-3((1(2sin(2π(-2|x| + 1) - 2) - 1) + 1)/(-3(2sin(2π(-2|x| + 1) - 2) - 1) + 4)) + 2)/(3((1(2sin(2π(-2|x| + 1) - 2) - 1) + 1)/(-3(2sin(2π(-2|x| + 1) - 2) - 1) + 4)) + 1) and g(x) = 3(2(-1x + 5) + 2)^2 - 1(2(-1x + 5) + 2... | 12 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (2(2(-1e^(2((-1x)/(1x))) - 3) - 4) + 2)/(-2(2(-1e^(2((-1x)/(1x))) - 3) - 4) - 1) and g(x) = (2((-1(-3x + 4) - 1)/(-1(-3x + 4))) + 3)/(3((-1(-3x + 4) - 1)/(-1(-3x + 4))) - 2) meet in the interval [-10, 10]?\n\nPresent... | 2 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = (2(-3(-2(-4x - 3)^2 + 3(-4x - 3) + 5) + 4))/(3(-3(-2(-4x - 3)^2 + 3(-4x - 3) + 5) + 4) - 1) and g(x) = -1|(2|(-1x - 3) - 1| + 3) - 3| - 1 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | -1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -3(-1|(1(4x^2 - 1x + 3) - 3) - 2|)^2 + 3(-1|(1(4x^2 - 1x + 3) - 3) - 2|) + 5 and g(x) = 2(-2|(-3x - 5) + 2| - 3) - 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 1 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -2sin(1π(-3|(1|(-1x - 4) - 1|)| - 1) + 3) + 3 and g(x) = 5(1((3x - 2)/(-2x)) - 1) + 5 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -3(-4(-2e^(1((2x + 2)/(2x - 1))))^2 + 2(-2e^(1((2x + 2)/(2x - 1)))) - 1) - 3 and g(x) = 3(-4((-1x + 1)/(-3x + 1)) - 5)^2 - 4(-4((-1x + 1)/(-3x + 1)) - 5) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{... | -3 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1|(-3|((-3(1x + 4) + 3)/(1(1x + 4) - 3)) - 2| + 2) - 3| - 2 and g(x) = (3((1(1x^2 - 1x) + 2)/(2(1x^2 - 1x) + 1)) - 1)/(-1((1(1x^2 - 1x) + 2)/(2(1x^2 - 1x) + 1)) + 3) intersect in the interval [-10, 10]?\n\nPresent the a... | 1 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -1|(-1sin(1π(-2|(2x + 5) - 2| - 2) - 1) + 3)| and g(x) = 1sin(1π(2(2x + 2)^2 - 5(2x + 2) + 2) - 2) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{... | 5 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -2((-3(1(4x + 5) + 1) - 2)/(-1(1(4x + 5) + 1) + 2))^2 + 2((-3(1(4x + 5) + 1) - 2)/(-1(1(4x + 5) + 1) + 2)) and g(x) = 2((3((1x + 2)/(-1x + 2)) + 3)/(2((1x + 2)/(-1x + 2)) + 2)) - 3 meet in the interval [-10, 10] and round to the neares... | -4 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (3((1(-2(3x^2 + 3x - 1)^2 - 4(3x^2 + 3x - 1) + 3) - 1)/(1(-2(3x^2 + 3x - 1)^2 - 4(3x^2 + 3x - 1) + 3))) + 2)/(-2((1(-2(3x^2 + 3x - 1)^2 - 4(3x^2 + 3x - 1) + 3) - 1)/(1(-2(3x^2 + 3x - 1)^2... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -4(-2cos(2π((-2(2|x| + 3) - 3)/(-3(2|x| + 3))) - 2))^2 + 5 and g(x) = 1((2(-1x + 4))/(2(-1x + 4))) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (3(-4((2((2x - 2)/(2x - 3)) - 2)/(1((2x - 2)/(2x - 3)))) + 4))/(-3(-4((2((2x - 2)/(2x - 3)) - 2)/(1((2x - 2)/(2x - 3)))) + 4) - 3) and g(x) = -1(-3(-5x + 3)^2 - 4(-5x + 3)) meet in the interval [-10, 10] and round to the nearest intege... | 1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (-3((2(5(1x^2 - 1x - 4) + 3) - 1)/(1(5(1x^2 - 1x - 4) + 3) + 3)) + 2)/(-2((2(5(1x^2 - 1x - 4) + 3) - 1)/(1(5(1x^2 - 1x - 4) + 3) + 3)) - 3) and g(x) = 1|(-2|(-1|x + 3|) + 1| - 3) - 3| - 3 meet in the interval [-10, 10].\n\n... | 2 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 2(3e^(2((3(-2|x + 3| + 2) - 1)/(3(-2|x + 3| + 2) - 2))) + 1)^2 - 2(3e^(2((3(-2|x + 3| + 2) - 1)/(3(-2|x + 3| + 2) - 2))) + 1) - 4 and g(x) = (3(1(-3x + 3) + 5) + 1)/(-1(1(-3x + 3) + 5)) i... | -2 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -1|(2(1(-1sin(2πx - 3) + 1) - 2) - 4) - 1| and g(x) = (-3(3(-4x + 5) - 3) + 3)/(2(3(-4x + 5) - 3) + 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = (-1(2|(1|(-2cos(3πx + 1) - 1) + 2| + 1) - 2|) - 2)/(-3(2|(1|(-2cos(3πx + 1) - 1) + 2| + 1) - 2|) - 2) and g(x) = 2(1((1x + 3)/(-2x + 1)) + 2) + 4 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -2|(2(-2(-3|x - 1| + 2)^2 + 2(-3|x - 1| + 2) - 3)^2 - 1(-2(-3|x - 1| + 2)^2 + 2(-3|x - 1| + 2) - 3) - 3) - 3| - 3 and g(x) = (-2(2sin(1π((1x + 2)/(-1x - 3)) + 2) - 1))/(-1(2sin(1π((1x + 2)/(-1x - 3)) + 2) - 1) - 2) inter... | 2 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -1|((1((1(-2|x + 3|) - 2)/(-2(-2|x + 3|) + 3)) + 3)/(3((1(-2|x + 3|) - 2)/(-2(-2|x + 3|) + 3)) + 2)) - 1| + 2 and g(x) = (2(1(-5x + 5) + 1) - 2)/(-2(1(-5x + 5) + 1)) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex ... | 1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -4((2(-2((-1x + 1)/(-1x - 1))^2 + 4((-1x + 1)/(-1x - 1)) + 4) + 3)/(-2(-2((-1x + 1)/(-1x - 1))^2 + 4((-1x + 1)/(-1x - 1)) + 4) - 3)) - 4 and g(x) = -1((-2(3x^2 - 2x + 1) + 3)/(1(3x^2 - 2x + 1) +... | 0 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -2(3|(-3|(1x - 3) - 1| - 3) - 1| - 1) and g(x) = -5((-3((1x)/(2x - 1)) + 2)/(3((1x)/(2x - 1)) - 1)) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -4(1(1(-2e^(2x))^2 + 4(-2e^(2x)) - 4)^2 + 2(1(-2e^(2x))^2 + 4(-2e^(2x)) - 4) + 5) + 1 and g(x) = -5((3(-3x^2 + 3x + 4) + 3)/(2(-3x^2 + 3x + 4) + 1)) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your ... | -1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -2|((1((2(-2sin(2πx + 3) + 2) + 3)/(1(-2sin(2πx + 3) + 2) + 1)) + 3)/(2((2(-2sin(2πx + 3) + 2) + 3)/(1(-2sin(2πx + 3) + 2) + 1)) + 1)) + 1| - 3 and g(x) = -1e^(-1(-5(1x^2 + 4x - 1) + 5)) + 2 in the interv... | 1 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -4(-2e^(2((-1(2x^2 + 1x - 3) - 3)/(-1(2x^2 + 1x - 3) + 2))) + 3)^2 - 1(-2e^(2((-1(2x^2 + 1x - 3) - 3)/(-1(2x^2 + 1x - 3) + 2))) + 3) - 1 and g(x) = -1|(4((-2x - 3)/(2x + 2))^2 + 1((-2x - 3)/(2x + 2)) - 2) - 2| + 1 meet in ... | -1 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1(1(-1|(-3x + 5) + 2|)^2 - 1)^2 - 3(1(-1|(-3x + 5) + 2|)^2 - 1) + 3 and g(x) = 2|(-3(2|x - 3|)^2 - 3(2|x - 3|))| - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -4(-2sin(2π(-3|(2|x - 2| - 1) + 2| + 2) + 2) - 1) + 1 and g(x) = -3(1((3x + 2)/(2x - 1))^2 + 3((3x + 2)/(2x - 1)) + 1)^2 - 4(1((3x + 2)/(2x - 1))^2 + 3((3x + 2)/(2x - 1)) + 1) - 4 intersect in the interval [-10, 10]?\n\nP... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -3e^(-2(1|(-5(-5x - 2))| - 2)) - 1 and g(x) = -2(1(2x^2 - 3x + 3) - 2)^2 - 2(1(2x^2 - 3x + 3) - 2) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1sin(1π(-4(-1|(-5x - 2) + 2| + 1)^2 - 4(-1|(-5x - 2) + 2| + 1) - 2) + 3) - 1 and g(x) = -3e^(2(-4(-2x - 1)^2 + 4(-2x - 1) + 4)) + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxe... | -1 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -3((3(-2(-4x^2 + 5x - 4) - 2) + 2)/(2(-2(-4x^2 + 5x - 4) - 2) - 1))^2 + 3((3(-2(-4x^2 + 5x - 4) - 2) + 2)/(2(-2(-4x^2 + 5x - 4) - 2) - 1)) + 3 and g(x) = (-3(1|(-1|x + 1| - 1) - 3|) + 2)/(3(1|(-1|x + 1| - 1) - 3|) ... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (2((-3(4(5x^2 - 3x - 4) + 2) - 1)/(3(4(5x^2 - 3x - 4) + 2) - 1)) + 3)/(1((-3(4(5x^2 - 3x - 4) + 2) - 1)/(3(4(5x^2 - 3x - 4) + 2) - 1)) + 2) and g(x) = (2(1|(-1cos(1πx + 2))| - 1) - 3)/(1(1|(-1cos(1πx + 2))| - 1) + 2) inte... | -1 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (1(-2(-3((-3x + 1)/(-2x)) + 5)) - 3)/(1(-2(-3((-3x + 1)/(-2x)) + 5)) + 3) and g(x) = -5(-2(1x + 2)^2 - 5(1x + 2) - 2)^2 + 5(-2(1x + 2)^2 - 5(1x + 2) - 2) + 1 meet in the interval [-10, 10] and round to the nearest integer, what do you ... | -7 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (1(-2|(-2|(1x) - 1| + 1) - 1|) + 3)/(2(-2|(-2|(1x) - 1| + 1) - 1|) + 2) and g(x) = (-3((-3(2|x - 1| + 3) - 3)/(3(2|x - 1| + 3) + 3)) - 3)/(2((-3(2|x - 1| + 3) - 3)/(3(2|x - 1| + 3) + 3)) ... | 2 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1(2(2|((-3x - 1)/(2x + 1)) + 1|)^2 + 1(2|((-3x - 1)/(2x + 1)) + 1|) + 3) - 2 and g(x) = 3|(-4(5x^2 - 1x + 1) + 4) - 3| + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer... | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 1(-2(1(1e^(-1x) + 1) + 1) + 4)^2 + 5(-2(1(1e^(-1x) + 1) + 1) + 4) - 4 and g(x) = 4(1|(3x - 1)| - 1)^2 + 5(1|(3x - 1)| - 1) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -2 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 1|(1sin(1π(-2(-3|x - 1| - 1) - 4) - 1) - 2) - 2| + 2 and g(x) = (3(2(-4x^2 - 2x - 1)^2 - 2(-4x^2 - 2x - 1) - 3) - 2)/(-1(2(-4x^2 - 2x - 1)^2 - 2(-4x^2 - 2x - 1) - 3) + 2) meet in the interval [-10, 10] and round to the nearest integer,... | 0 | MATH |
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