Writing composite functions | Maths | Quizalize & Oak National Academy

Starter quiz

For the function $\text{f}(x)$ if $\text{f}(10)=35$ then $10$ is a value in the...

expression

domain ✓

range

output
Simplify $3x + 12 - x - 7$ .

$2x-5$

$2x+5$ ✓

$4x+19$

$8$

$3x+5$
Simplify $4(x-3)+x-3$ .

$5x-6$

$5(x-3)$ ✓

$5x-15$ ✓

$5x+15$

$3x-15$
Expand and simplify $(x+5)^2+(x+5)$ .

$4x^2+100$

$x^2+11x+30$ ✓

$x^2+10x+25$

$2x^2+10x+30$

$2(x+5)^2$
Expand and simplify $2(x+5)-(x+8)$ .

$4$

$2x+18$

$x+18$

$x+2$ ✓

$2x+2$
If $\text{f}(x)=5x$ , $\text{g}(x)=3x+4$ and $\text{h}(x)=1-2x$ evaluate and order the below from greatest to smallest value.

1

⇔

$\text{g}(3)$

2

⇔

$\text{f}(2)$

3

⇔

$\text{h}(-3)$

4

⇔

$\text{h}(1)$

5

⇔

$\text{g}(-2)$

6

⇔

$\text{f}(-1)$

Exit quiz

__________ function is where another function is applied to the output of a function.

An algebraic

An inverse

A composite ✓
Match the notation to the correct language.

${\text{fg}}(8)$

⇔

The output of ${\text{g}}(8)$ being input in to ${\text{f}}(x)$ ✓

${\text{gf}}(8)$

⇔

The output of ${\text{f}}(8)$ being input in to ${\text{g}}(x)$ ✓

${\text{hg}}(8)$

⇔

The output of ${\text{g}}(8)$ being input in to ${\text{h}}(x)$ ✓

${\text{gh}}(8)$

⇔

The output of ${\text{h}}(8)$ being input in to ${\text{g}}(x)$ ✓

${\text{ff}}(8)$

⇔

The output of ${\text{f}}(8)$ being input in to ${\text{f}}(x)$ ✓
If ${\text{f}}(x)=2x$ and ${\text{g}}(x)=5x-1$ then ${\text{fg}}(5)=$ ______.

'48' ✓
If ${\text{f}}(x)=2x$ and ${\text{g}}(x)=5x-1$ then ${\text{gf}}(5)=$ ______.

'49' ✓
If ${\text{f}}(x)=9x$ and ${\text{g}}(x)=3-2x$ how do we express the function ${\text{fg}}(x)$ ?

${\text{fg}}(x)=9(3-2x)$ ✓

${\text{fg}}(x)=3-18x$

${\text{fg}}(x)=27-18x$ ✓

${\text{fg}}(x)=3-9x$

${\text{fg}}(x)=27-2x$
If ${\text{f}}(x)=x^2$ and ${\text{g}}(x)=3-2x$ , how do we express the function ${\text{fg}}(x)$ ?

${\text{fg}}(x)=3-2x^2$

${\text{fg}}(x)=(3-2x)^2$ ✓

${\text{fg}}(x)=3-2(x^2)$

${\text{fg}}(x)=9+4x^2$

${\text{fg}}(x)=9-12x+4x^2$ ✓

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Video

Lesson Details

Key learning points

Using function notation, you can write a composite function.
Function notation can be replaced with the algebraic form.
An input can be substituted in and the numerical output found.

Common misconception

Pupils may try to evaluate composite functions by working from left to right.

Remind pupils that they cannot do this as each function needs an input and with composite functions the input needs to be evaluated before it can be used.

Keywords

Composite function - The composite function gf( $x$ ) is the combination of f( $x$ ) and g( $x$ ). The output from f( $x$ ) is the input for g( $x$ ).