In mathematics, a function domain is a description of the possible input values to a function.

Given a function fA → 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 gA → B, and S ⊆ A. Then the restriction of g to S is written:

g|S: SB

See also: Function codomain, Function range, Injective, Surjective, Bijective