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. It is sometimes denoted by or , where f is the function. In layman's terms, the domain of a function can generally be thought of as "what x can be".[1]
More precisely, given a function , the domain of f is X. In modern mathematical language, the domain is part of the definition of a function rather than a property of it.
In the special case that X and Y are both sets of real numbers, the function f can be graphed in the Cartesian coordinate system. In this case, the domain is represented on the x-axis of the graph, as the projection of the graph of the function onto the x-axis.
For a function , the set Y is called the codomain: the set to which all outputs must belong. The set of specific outputs the function assigns to elements of X is called its range or image. The image of f is a subset of Y, shown as the yellow oval in the accompanying diagram.
Any function can be restricted to a subset of its domain. The restriction of to , where , is written as .
^"Domain, Range, Inverse of Functions". Easy Sevens Education. Retrieved 2023-04-13.
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