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
    h(x)=5x−2h(x) = 5x - 2

    Solve h−1(x)=3h^{-1}(x) = 3
    Level 5 · 3 marksTry it
  2. 2
    f(x)=4−xf(x) = 4 - x

    (a) Find f−1(x)f^{-1}(x)

    (b) What do you notice about ff and f−1f^{-1}?
    Level 5 · 3 marksTry it
  3. 3
    f(x)=3x−1x+2f(x) = \dfrac{3x - 1}{x + 2}

    Find f−1(x)f^{-1}(x)
    Level 5 · 3 marksTry it
  4. 4
    f(x)=10x−3f(x) = \dfrac{10}{x - 3} for x≠3x \neq 3

    Find f−1(x)f^{-1}(x)
    Level 5 · 3 marksTry it
  5. 5
    f(x)=2x+cf(x) = 2x + c, where cc is a constant.

    f−1(11)=4f^{-1}(11) = 4

    Work out the value of cc.
    Level 5 · 3 marksTry it