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.