# Inverse Functions

## Prerequisites

### Inverse Functions

#### Introduction

• If f is a function, then its inverse function g is defined as the reverse of the mapping created by f. • If g is an inverse of f then: • and: #### Example

• To find the inverse of a function given as an equation, we can simply solve for y #### Notation

To denote that a function is an inverse of another, two different notations are commonly used:
• If the function is representedby the letter f then its inverse is can be denoted using a superscript of -1 `LaTeX:`f^{-1}(x)``
• If the function is represented by the letter f then its inverse is can be denoted using the letter g `LaTeX:`g(x)``

#### Properties

• If the original function is a bijection then its inverse will also be a bijection.
• If the original function is not a bijection then there is no guarantee that it has an inverse.
• If it is not injective then there may be two elements in the domain that map to the same element in the codomain.
• If it is not surjective then there may be an element in the codomain that is not mapped to from the domain.