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Domain (mathematics)
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Domain (mathematics)

In mathematics, the domain of a function is the set of all input values to the function.

Given a function , 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:

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:

The domain of given function can be restricted to a subset. Suppose that , and . Then the restriction of g to S is written:

See also

codomain, range of a function, injective function, surjective function, bijective function