Function domain
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