If f is a function of \(\mathbb{R}\) in \(\mathbb{R}\) that is not zero in \(\mathbb{R}\), then the inverse function of f is the new function g defined by \(g\left( x \right)= \dfrac {1}{f \left( x\right)}\).
- The functions f and g are inverses of each other if, for all elements in their domain, f(x) × g(x) = 1.
- The expression “inverse function” is a synonym for “the inverse of a function“.
Educational note
The inverse of a function should not be confused with the reciprocal of a function.