### 1) Composite functions

Two functions can be composed to form a new** composite function**. To write the composition of functions and , write or . A composite function is sometimes called a **compound function**.

**Question 1**

Find the composition of the two functions:

and .

.

Notice that .

If you’re feeling confident, try this more difficult example. Don’t be worried if it looks hard, the process you go through is just the same as before. Replace with the function and then simplify.

Consider the functions and . Find .

**Question 2**

, find

You now need to simplify the numerator and denominator separately.

Numerator

Denominator

Therefore,