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A function f from X to Y. The set of points in the red oval X is the domain of f. Graph of the real-valued square root function, f(x) = √ x, whose domain consists of all nonnegative real numbers. In mathematics, the domain of a function is the set of inputs accepted by the function.
is a function from domain X to codomain Y. The yellow oval inside Y is the image of . Sometimes "range" refers to the image and sometimes to the codomain. In mathematics, the range of a function may refer to either of two closely related concepts: the codomain of the function, or; the image of the function.
On the other hand, if a function's domain is continuous, a table can give the values of the function at specific values of the domain. If an intermediate value is needed, interpolation can be used to estimate the value of the function. For example, a portion of a table for the sine function might be given as follows, with values rounded to 6 ...
The image of a function is the image of its entire domain, also known as the range of the function. [3] This last usage should be avoided because the word "range" is also commonly used to mean the codomain of .
The term range is sometimes ambiguously used to refer to either the codomain or the image of a function. A codomain is part of a function f if f is defined as a triple ( X , Y , G ) where X is called the domain of f , Y its codomain , and G its graph . [ 1 ]
Sigmoid functions have domain of all real numbers, ... in the range 0 to 1. Another commonly used range is from −1 to 1. ... The logistic function can be calculated ...
For all inverse hyperbolic functions, the principal value may be defined in terms of principal values of the square root and the logarithm function. However, in some cases, the formulas of § Definitions in terms of logarithms do not give a correct principal value, as giving a domain of definition which is too small and, in one case non-connected.
The domain of f is the set of complex numbers such that (). Every rational function can be naturally extended to a function whose domain and range are the whole Riemann sphere (complex projective line). Rational functions are representative examples of meromorphic functions.
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