GCSE · Functions

Inverse functionsExam-style questions

Why f⁻¹ runs the machine backwards (and is NOT 1/f), the write-swap- rearrange recipe for finding it, and the ff⁻¹(x) = x check that catches every error.

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

DifficultyAllLevel 4Level 5
  1. 1
    f(x)=2x+5f(x) = 2x + 5

    Find f−1(x)f^{-1}(x)
    Level 4 · 2 marksTry it
  2. 2
    g(x)=x−43g(x) = \dfrac{x - 4}{3}

    (a) Find g−1(x)g^{-1}(x)

    (b) Work out g−1(2)g^{-1}(2)
    Level 4 · 3 marksTry it
  3. 3
    f(x)=x4+3f(x) = \dfrac{x}{4} + 3

    (a) Find f−1(x)f^{-1}(x)

    (b) Work out f−1(5)f^{-1}(5)
    Level 4 · 3 marksTry it
  4. 4
    g(x)=3(x−2)g(x) = 3(x - 2)

    (a) Find g−1(x)g^{-1}(x)

    (b) Solve g−1(x)=10g^{-1}(x) = 10
    Level 4 · 4 marksTry it
  5. 5
    f(x)=6x−1f(x) = 6x - 1

    (a) Find f−1(x)f^{-1}(x)

    (b) Show that f ⁣(f−1(x))=xf\!\left(f^{-1}(x)\right) = x
    Level 4 · 4 marksTry it