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A function or mapping for which more than one element of the domain maps onto an element in the range. So f(x)=x2 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)=x2 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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