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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.
Given its domain and its codomain, a function is uniquely represented by the set of all pairs (x, f (x)), called the graph of the function, a popular means of illustrating the function. [note 1] [4] When the domain and the codomain are sets of real numbers, each such pair may be thought of as the Cartesian coordinates of a point in the plane.
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.
The function is surjective, or onto, if each element of the codomain is mapped to by at least one element of the domain; that is, if the image and the codomain of the function are equal. A surjective function is a surjection. [1] Notationally:
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.
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 ...
In other words, every element of the function's codomain is the image of at most one element of its domain. Surjective function : has a preimage for every element of the codomain , that is, the codomain equals the image.
The image of a function of a real variable is a curve in the codomain. In this context, a function that defines curve is called a parametric equation of the curve. When the codomain of a function of a real variable is a finite-dimensional vector space, the function may be viewed as a sequence of real functions. This is often used in applications.