**f(x)**, we can find the inverse function

**f**.

^{−1}(x)## How to Find the Inverse of a Function

Finding the inverse of a function is easy.## Question

Find the inverse function of the function below.## Step-by-Step:

## 1

Rearrange the function to find

We have rearranged

**"x ="**.f(x) = ½x + 1 | |

f(x) − 1 = ½x + 1 − 1 |
Subtract 1 from both sides |

f(x) − 1 = ½x | |

2 × ( f(x) − 1 ) = 2 × ½x |
Multiply both sides by 2 |

2( f(x) − 1 ) = x | |

x = 2( f(x) − 1 ) |

**f(x) = ½x + 1**to find what**"x = "**.**x = 2( f(x) − 1 )**## 2

Replace

**x**with**f**.^{−1}(x)**f**= 2( f(x) − 1 )

^{−1}(x)## 3

Replace

**f(x)**with**x**.
f

^{−1}(x) = 2(**x**− 1 )## Answer:

The inverse of the function**f(x) = ½x + 1**is:

**f**.

^{−1}(x) = 2(x − 1)## Why Do We Relabel the Input and the Output?

When we find the inverse of a function, we replace:- the input of the function (
**x**) with the output of the inverse function (**f**), and^{−1}(x) - the output of the function (
**f(x)**) with the input of the inverse function (**x**).

- An inverse function reverses a function, relating the function's output
**f(x)**to its input**x**. We can think of**f(x)**being the input to the inverse function and**x**being its output. - An inverse function is a function. Using functional notation, an inverse function relates an input
**x**to an output**f**.^{−1}(x)

**f(x)**with

**x**and

**x**with

**f**.

^{−1}(x)## You might also like...

functionsunderstanding inverse functionsfinding the inverse of a function using a graphfractions curriculum

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