
inverse function


A function, usually written as f^{1}, that exactly reverses the mapping produced by a given function f. The "1" above the function stands for an inverse function and has nothing to do with a "1" used as an exponent.
For example, f(x) = x^{1/3} and g(x) = x^{3} are inverse functions because g(x) always exactly reverses the mapping done by f(x). For any number a, f(a) = a^{1/3}. The reverse operation gives g(f(a)) = g(a^{1/3}) = (a^{1/3})^{3} = a.

