Assertion: function's domain | /r/HasProperty | real numbers
Facets:
value: with a finite number of them
type: OTHER
value: except for 1
type: OTHER
value: except for x=1
type: OTHER
value: for many commonly used real functions
type: OTHER
value: in each of the above problems
type: OTHER
value: with the exception of the division
type: OTHER
value: except for 0
type: OTHER
value: including 6
type: OTHER
Source sentences:
text: The Domain (all the values that can go into the function) is all Real Numbers up to and including 6, which we can write like this:
text: Which says "the domain of f plus g is the set of all Real Numbers that are in the domain of f
text: For example, a "function from the reals to the reals" may refer to a real-valued function of a real variable, and this phrase does not mean that the domain of the function is the whole set of the real numbers, but only that the domain is a set of real numbers that contains a non-empty open interval; such a function is then called a partial function.
text: For many commonly used real functions, the domain is the whole set of real numbers, and the function is continuous and differentiable at every point of the domain.
text: Since there is no natural restriction on the values of x, the natural domain of that function is any real number.
text: This means the domain or input of f is a real number R and the range or output of f is also a real number R.
text: x ↦ 1 x , {\displaystyle x\mapsto {\frac {1}{x}},} whose graph is a hyperbola, and whose domain is the whole real line except for 0.
text: When the domain and the codomain are sets of real numbers, each such pair may be considered as the Cartesian coordinates of a point in the plane.
text: If the domain of a function is a subset of the real numbers and the function is represented in a Cartesian coordinate system, then the domain is represented on the x-axis.
text: For example, a "function from the reals to the reals" may refer to a real-valued function of a real variable, and this phrase does not mean that the domain of the function is the whole set of the real numbers, but only that the domain is a set of real numbers that contains a non-empty open interval; such a function is then called a partial function.
text: For instance the natural domain of square root is the non-negative reals when considered as a real number function.
text: Therefore the domain is all real numbers greater than or equal to 2.
text: In each of the above problems, the domain is all real numbers with the exception of the division.
text: The domain in the division combination is all real numbers except for 1 and -1.
text: All other real numbers are valid inputs, so the domain is all real numbers except for x=1.
text: Domain and range are real numbers
text: In mathematical analysis, and applications in geometry, applied mathematics, engineering, and natural sciences, a function of a real variable is a function whose domain is the real numbers ℝ, or a subset of ℝ that contains an interval of positive length.
text: Rational functions are quotients of two polynomial functions, and their domain is the real numbers with a finite number of them removed to avoid division by zero.
text: Its domain is the set of all real numbers different from − d / c , {\displaystyle -d/c,} and its image is the set of all real numbers different from a / c .
text: It is quite common for the domain to be the set of all real numbers since many mathematical functions can accept any input.
text: For instance, the domain of cosine is the set of all real numbers, while the domain of the square root consists only of numbers greater than or equal to 0 (ignoring complex numbers in both cases).
text: A real function is a real-valued function of a real variable, that is, a function whose codomain is the field of real numbers and whose domain is a set of real numbers that contains an interval.
text: The polynomial functions are defined by polynomials, and their domain is the whole set of real numbers.