## Quick Reference

A function from the set **R** of real numbers (or a subset of **R**) to **R**. Thus, if *f* is a real function, then, for every real number *x* in the domain, a corresponding real number *f*(*x*) is defined. In analysis, a function *f*: *S* → **R** is often defined by giving a formula for *f*(*x*), without specifying the domain *S* (see function). In that case, it is usual to assume that the domain is the largest possible subset *S* of **R**. For example, if *f*(*x*)=1/(*x*−2), the domain would be taken to be **R**\ {2}; that is, the set of all real numbers not equal to 2. If *f*(*x*) = √9 − *x*^{2}, the domain would be the closed interval [−3, 3].

*Subjects:*
Mathematics.

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