Function of a real variable
Domain

The domain of a function of several real variables is a subset of R {\displaystyle \mathbb {R} } that is sometimes explicitly defined. In fact, if one restricts the domain X of a function f to a subset Y ⊂ X, one gets formally a different function, the restriction of f to Y, which is denoted f. In practice, it is often not harmful to identify f and f, and to omit the subscript.

Conversely, it is sometimes possible to enlarge naturally the domain of a given function, for example by continuity or by analytic continuation. This means that it is not worthy to explicitly define the domain of a function of a real variable.
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