Domain (mathematics)

In Mathematics , the domain of a Function is the set of all input values to the function. DOMAIN OF A FUNCTION Given a function ''f'':''X''→''Y'', the set ''X'' 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}. Sometimes the codomain is incorrectly called the range because of a failure to distinguish between possible and actual values. A well-defined function must map every element of the domain to an element of its codomain. For example, the function ''f'' defined by : ''f''(''x'') = 1/''x'' has no value for ''f''(0). Thus, the set R of Real Number s cannot be its domain. In cases like this, the function is usually either defined on R\{0}, or the "gap" is plugged by specifically defining ''f''(0). If we extend the definition of ''f'' to : ''f''(''x'') = 1/''x'', for ''x'' ≠ 0 : ''f''(0) = 0, then ''f'' is defined for all real numbers and we can choose its domain to be R. Any function can be restricted to a Subset of its domain.
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