### Prerequisite Material:

### Composite Functions:

Definition: a function made of up of two or more other functions, where the output of one is the input to the other and so on.

Example:

If
$f\left(x\right)=x+2$,
then
$f\left(3\right)=3+2=5$.

We could take this output and enter it into another function, say,
$g\left(x\right)=3x-4$.

Entering the value from $f\left(x\right)$, then
$g\left(5\right)=3\times 5-4=11$.

The same result can be found by substituting $f\left(x\right)$ into $g\left(x\right)$

$g\left(f\left(x\right)\right)=g(x+2)=3(x+2)-4=3x+2$

So, if
$x=3$
then
$g\left(f\left(3\right)\right)=3\times 3+2=11$.

That is the same as before.

An alternate way of writing
$g\left(f\left(x\right)\right)$
can be written as
$gf\left(x\right)$.

Note: the function $f$ is worked out before $g$.

In general $gf\left(x\right)$ is not the same as $fg\left(x\right)$.

### Questions:

Questions

Practice Questions from corbettmaths.com

Textbook Questions from corbettmaths.com

GCSE Questions & Answers from piacademy.co.uk

Further Maths Video from corbettmaths.com

Further Maths Practice Questions from corbettmaths.com