If and are inverses, then

### Creating Inverse Functions

We know that when a function is composed into its inverse the result is just . How do we create inverse functions though?

**Step 1:** Change into a

**Step 2:** Switch and

**Step 3:** Solve for . You should get

**Step 4:** replace with

**Example**: Find the inverse of

Graphs of Inverse Functions}

Graphs of inverse functions are always *reflections* over the line (yes, the same that’s a solution when we find they’re inverses).

Another way of saying this is that if is a point

That’s another way of saying: switch the and .

**Example 1)**

The values of the points are reversed. There is also a reflection over the line