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

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
  4. 4
    f(x)=2x+3g(x)=x2−1\mathrm{f}(x) = 2x + 3 \qquad \mathrm{g}(x) = x^2 - 1

    (a) Show that gf(x)=4x2+12x+8\mathrm{gf}(x) = 4x^2 + 12x + 8 (2 marks)

    (b) Solve gf(x)=8\mathrm{gf}(x) = 8 (2 marks)
    Level 4 · 4 marksTry it
  5. 5
    f(x)=3x−1g(x)=x2+1\mathrm{f}(x) = 3x - 1 \qquad \mathrm{g}(x) = x^2 + 1

    (a) Work out fg(2)\mathrm{fg}(2). [2]

    (b) Solve fg(x)=gf(x)\mathrm{fg}(x) = \mathrm{gf}(x). [3]
    Level 4 · 5 marksTry it

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