#### 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 -1LaTeX:

`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.