# High School Math : Understanding Inverse Functions

## Example Questions

### Example Question #1 : Understanding Inverse Functions

Let . What is ?

Explanation:

We are asked to find , which is the inverse of a function.

In order to find the inverse, the first thing we want to do is replace f(x) with y. (This usually makes it easier to separate x from its function.).

Next, we will swap x and y.

Then, we will solve for y. The expression that we determine will be equal to .

Subtract 5 from both sides.

Multiply both sides by -1.

We need to raise both sides of the equation to the 1/3 power in order to remove the exponent on the right side.

We will apply the general property of exponents which states that .

Laslty, we will subtract one from both sides.

The expression equal to y is equal to the inverse of the original function f(x). Thus, we can replace y with .

The answer is .

### Example Question #2 : Understanding Inverse Functions

What is the inverse of ?

Explanation:

The inverse of requires us to interchange and and then solve for .

Then solve for :

If , what is ?