# How do you find the inverse of #f(x) = 5x^3 - 7#?

##### 1 Answer

**Inverse of the function**

#### Explanation:

**Note:**

The **Inverse** of a function may NOT always be a function.

So, if the inverse of a function is a function by itself, then it is called an **Inverse Function**.

**How do we determine these inverse relationships ?**

**Method 1**

We can find the inverse of the function by simply swapping the ordered pairs.

**Method 2**

(a) Set the function to

(b) Swap the

(c) Solve for

**Method 3**

**The graph of an inverse function is the reflection ** of the original graph over the line **Identity Line**.

**Given the function :**

Construct a **data table** for this function and **graph it**.

Behavior of the **Parent Graph** shown

We use the **Method 2** to solve

(a) Set the function to

(b) Swap the

(c) Solve for

We have,

Subtract

Subtract

Multiply both sides by

Divide both sides by

Take **Cube Root** on both sides

**Cube** and the **Cube Root** cancel each other.

Hence,

**Inverse of the function**

Explore the graph: