Main Page | See live article | Alphabetical index In mathematics, a function domain is a description of the possible input values to a function. Given a function f: A → B, the set A is called the domain, or domain of definition of f. The set of all values in the codomain that f maps to is called the range of f, or f(A). A well-defined function must map every element of the domain to an element of its codomain. So, for example, the function: f: x → 1/x has no valid value for f(0). It is thus not a function on the set R of real numbers; R can't be its domain. It is usually either defined as a function on R \\ {0}, or the "gap" is plugged by specifically defining f(0); for example: f: x → 1/x , x ≠ 0 f: 0 → 0 The domain of given function can be restricted to a subset. Suppose that g: A → B, and S ⊆ A. Then the restriction of g to S is written: g|S: S → B See also: Function codomain, Function range, Injective, Surjective, Bijective This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.