# Domain of a function

## Mathematical concept / From Wikipedia, the free encyclopedia

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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.

More precisely, given a function , the domain of *f* is *X*. Note that 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 subsets of , 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*, and the set of values attained by the function (which is a subset of *Y*) is called its *range* or *image*.

Any function can be restricted to a subset of its domain. The restriction of to , where , is written as .