# 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 #1661 : High School Math

What is the inverse of ?      Explanation:

The inverse of requires us to interchange and and then solve for .  Then solve for : ### Example Question #1661 : High School Math

If , what is ?      Explanation:

To find the inverse of a function, exchange the and variables and then solve for .   ### All High School Math Resources 