# Inverse Function

## Inverse Function

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.