**Composite** functions involve 2 (or more) functions carried out in a sequence.

**As an example, let's say that f(x) = x + 1 and g(x) = x² - 3. Find fg(5). **

**fg(x) **means carry out **g(x)** first and then we need to put our output into **f(x)**.

The first function we need to deal with is the one **closest to (x)**, and work through them from left to right.

First, let's find **g(5)**:

g(5) = 5² - 3 = 25 - 3 = 22

Now let's put our output into f(x):

f(22) = 22 + 1 = 23

**So fg(5) = 23**

If we change the order, our answer will be different, so always check carefully which function you need to start with.

Just to prove this, let's consider **gf(5)**.

f(5) = 5 + 1 = 6

g(6) = 6² - 3 = 36 - 3 = 33

**So gf(5) = 33**

In this activity, we will find outputs from composite functions involving up to three separate functions carried out in a sequence, correctly prioritising their order based on their proximity to **(x)**.