## Quick Reference

A function or mapping for which more than one element of the domain maps onto an element in the range. So *f*(*x*)=*x*^{2} is many-to-one if *x* is defined on the real numbers since *f*(*a*)=*f*(−*a*). A many-to-one function is not invertible, since there is no way to define a function to return more than one value. However, a many-to-one function can be restricted to a domain within which it is a one-to-one function, and for which the inverse function exists. If *f*(*x*)=*x*^{2} is restricted to *x*≥0 then *f*^{−1}(*x*) = √*x* exists. Electronic calculators do this by default, for example the trigonometric functions will return inverse values over an interval of width 180° or π radians.

*Subjects:*
Mathematics.

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