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.

Start practising Read the lesson

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

DifficultyAllLevel 3Level 4Level 5
  1. 1
    The functions f\mathrm{f} and g\mathrm{g} are such that

    f(x)=3x−2g(x)=x2+1\mathrm{f}(x) = 3x - 2 \qquad \mathrm{g}(x) = x^2 + 1
    (a) Find fg(4)\mathrm{fg}(4) (2 marks)
    (b) Find f−1(x)\mathrm{f}^{-1}(x) (2 marks)
    Level 3 · 4 marksTry it
  2. 2
    f(x)=x−1f(x) = x - 1 and g(x)=4xg(x) = 4x

    (a) Work out gf(5)gf(5)

    (b) Work out fg(5)fg(5)
    Level 3 · 4 marksTry it
  3. 3
    f(x)=3x−2f(x) = 3x - 2 and g(x)=x+5g(x) = x + 5

    (a) Work out fg(2)fg(2)

    (b) Work out gf(2)gf(2)
    Level 3 · 4 marksTry it