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A function f from X to Y.The blue oval Y is the codomain of f.The yellow oval inside Y is the image of f, and the red oval X is the domain of f.. In mathematics, a codomain or set of destination of a function is a set into which all of the output of the function is constrained to fall.
It is important to specify the domain and codomain of each function, since by changing these, functions which appear to be the same may have different properties. Injective and surjective (bijective) The identity function id X for every non-empty set X, and thus specifically :.
For some functions, the image and the codomain coincide; these functions are called surjective or onto. For example, consider the function () =, which inputs a real number and outputs its double. For this function, both the codomain and the image are the set of all real numbers, so the word range is unambiguous.
The preimage by f of an element y of the codomain is sometimes called, in some contexts, the fiber of y under f. If a function f has an inverse (see below), this inverse is denoted . In this case () may denote either the image by or the preimage by f of C. This is not a problem, as these sets are equal.
In mathematics, a surjective function (also known as surjection, or onto function / ˈ ɒ n. t uː /) is a function f such that, for every element y of the function's codomain, there exists at least one element x in the function's domain such that f(x) = y. In other words, for a function f : X → Y, the codomain Y is the image of the function ...
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
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.
A complex-valued function of a real variable may be defined by relaxing, in the definition of the real-valued functions, the restriction of the codomain to the real numbers, and allowing complex values. If f(x) is such a complex valued function, it may be decomposed as f(x) = g(x) + ih(x), where g and h are real-valued functions. In other words ...