Function domain
From Wikinfo
[[fr:Ensemble de d�finition]] [[sv:definitionsm�ngd]] 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
References
- Adapted from the Wikipedia article, "Function_domain" http://en.wikipedia.org/wiki/Function_domain, used under the GNU Free Documentation License
