Last updated on Sep 20, 2026

Algebra III (AQA GCSE Further Maths): Quizzes

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Composite functions

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What is a composite function?

Functions applied one after another

In $fg(x)$ , which function is applied first?

$g$

If $f(x) = x^2$ and $g(x) = x + 2$ , what is $fg(x)$ ?

$(x + 2)^2$

Why does order matter in composite functions?

$fg(x)$ and $gf(x)$ give different results

If $f(x) = x^2$ and $g(x) = x + 2$ , what is $gf(x)$ ?

$x^2 + 2$

For $(5x + 6)^4$ , if $g(x) = 5x + 6$ is applied first, what is $f(x)$ ?

$x^4$

If $f(x) = x^2$ and $g(x) = x + 2$ , what is $f(x) + g(x)$ ?

$x^2 + x + 2$

If $f(x) = x^2$ and $g(x) = x + 2$ , what is $f(x) \times g(x)$ ?

$x^3 + 2x^2$

In $fgh(x)$ , which function is applied first?

$h$

What does $f^2(x)$ mean?

$f(f(x))$

If $f(x) = 2x - 3$ , what is $f^2(x)$ ?

$4x - 9$

When substituting one function into another, what must you use to avoid mistakes?

Brackets

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