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0580/42 May/Jun 2026, Question 17: Functions

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 7 marks

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The question, in short

f(x) = 20 − 3x, g(x) = 64/2ˣ and h(x) = 7 + 2x. Find f(4), the inverse of h, gg(5), and solve g⁻¹(x) = 8.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

Find f(4).

  1. 1f(4) = 20 − 3 × 4 = 8

Answer8

Part (b) · 2 marks

Find h⁻¹(x).

  1. 1y = 7 + 2x, swap: x = 7 + 2y
  2. 22y = x − 7
  3. 3h⁻¹(x) = (x − 7)/2

Answer(x − 7)/2

Part (c) · 2 marks

Find gg(5).

  1. 1g(5) = 64/2⁵ = 64/32 = 2
  2. 2gg(5) = g(2) = 64/2² = 16

Answer16

Part (d) · 2 marks

Solve g⁻¹(x) = 8.

  1. 1g⁻¹(x) = 8 means x = g(8)
  2. 2x = 64/2⁸ = 64/256 = 1/4

Answer1/4 or 0.25

Stuck on a step? Read the free lesson: Inverse Functions

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Also searched as: 0580/42/M/J/26 · 0580_s26_qp_42 · 0580 s26 42 · question 17.
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