GCSE · Functions

Composite functionsExam-style questions

Why fg(x) means "g first, then f", how to chain outputs into inputs for numbers and for algebra, and why the order almost always matters.

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16 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
$\mathrm{f}(x) = 2x + 3 \qquad \mathrm{g}(x) = 4x^2 - 5$

Show that $\mathrm{gf}(x) = 2\mathrm{fg}(x)$ for exactly one value of $x$ .

(5 marks)
Level 5 · 5 marksTry it
2
$\mathrm{f}(x) = 5x - 4 \qquad \mathrm{h}(x) = 2x^2 + x$

Show that the equation $5\mathrm{fh}(x) = \mathrm{hf}(x)$ is satisfied by only one value of $x$ .

(5 marks)
Level 5 · 5 marksTry it
3
$f(x) = 2x + 1$ and $g(x) = x^2 - 3$

(a) Find $fg(x)$ , giving your answer in its simplest form.

(b) Find $gf(x)$ , giving your answer in its simplest form.
Level 5 · 4 marksTry it
4
$f(x) = 2x + 1$ and $g(x) = x^2 - 3$

Solve $fg(x) = 45$
Level 5 · 3 marksTry it
5
$f(x) = 2x + 1$

(a) Find $ff(x)$ , giving your answer in its simplest form.

(b) Solve $ff(x) = 23$
Level 5 · 4 marksTry it

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