Domain (mathematics)

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

Related Topics:
Mathematics - Function

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X, the set of input values, is called the domain of f, and Y, the set of possible output values, is called the codomain. The range of f is the set of all actual outputs {f(x) : x in the domain}. Beware that sometimes the codomain is incorrectly called the range because of a failure to distinguish between possible and actual values.

Related Topics:
Domain - Codomain - Range

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Given a function f : A → B, the set A is called the domain, or domain of definition of f.

Related Topics:
Function - Set

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The set of all values in the codomain that f maps to is called the range of f, written f(A).

Related Topics:
Codomain - Range

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A well-defined function must map every element of the domain to an element of its codomain.

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For example, the function f defined by

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: f(x) = 1/x

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has no value for f(0).

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Thus, the set R of real numbers cannot be its domain.

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In cases like this, the function is usually either defined on R{0}, or the "gap" is plugged by specifically defining f(0).

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If we extend the definition of f to

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: f(x) = 1/x, for x ≠ 0

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: f(0) = 0,

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then f is defined for all real numbers and we can choose its domain to be R.

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Any function can be restricted to a subset of its domain.

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The restriction of g : A → B to S, where S ⊆ A, is written g |S : S → B.

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Some well-known domains are as follows (note that each successive domain includes those above it):

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