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0580/23 May/Jun 2025, Question 22: Composite Functions

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 8 marks

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The question, in short

Given f(x) = 2x + 5, g(x) = x − 4 and h(x) = 5ˣ, evaluate, invert and solve equations involving these functions.

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

Part (a) · 1 mark

Find the value of f(3).

  1. 1f(3) = 2 × 3 + 5 = 11

Answer11

Part (b) · 2 marks

Find the inverse function f⁻¹(x).

  1. 1y = 2x + 5, so y − 5 = 2x
  2. 2x = (y − 5)/2
  3. 3f⁻¹(x) = (x − 5)/2

Answer(x − 5)/2

Part (c) · 3 marks

Solve the equation fg(x) = 25 for x.

  1. 1fg(x) = 2(x − 4) + 5 = 25
  2. 22x − 8 + 5 = 25, so 2x = 28
  3. 3x = 14

Answer14

Part (d) · 2 marks

Find the value of x for which h⁻¹(x) = 2.

  1. 1h⁻¹(x) = 2 means x = h(2)
  2. 2x = 5² = 25

Answer25

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Also searched as: 0580/23/M/J/25 · 0580_s25_qp_23 · 0580 s25 23 · question 22.
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