# How to Find the Inverse of a Function

## Finding the Inverse of a Function

An inverse function is a function that reverses another function.

If we have a function **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 **"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 ) |

We have rearranged **f(x) = ½x + 1** to find what **"x = "**.

**x = 2( f(x) − 1 )**

# 2

Replace **x** with **f ^{−1}(x)**.

**f ^{−1}(x)** = 2( f(x) − 1 )

# 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)**.