Inverse Functions

Inverse of a Function

Definition

A function is the inverse of a function is , for any in the domain of

In other words, we swap the domain and range. More formally, when we treat a function as a binary relation, then we are finding the inverse relation.

The inverse of is written as
- This is NOT the reciprocal of
- However, is understood as , whereas is the inverse and is the reciprocal

In simple cases the inverse can be found by solving the equation for

Example

Find the inverse of

So the inverse of is given by

Not every function possesses an Inverse, only injective functions

Example

The function has no inverse. However, restricting to the interval does have an inverse.