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4024/23 May/Jun 2026, Question 15: Composite Functions

Cambridge O Level Mathematics 4024 · Paper 23 (Calculator) · Calculator · 6 marks

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The question, in short

Given f(x) = 6x + 8 and g(x) = (x − 1)/3, evaluate f at −1, find the inverse of g, and solve the composite equation fg(x) = 14.

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Part (a) · 1 mark

Calculate the value of f(−1) using f(x) = 6x + 8.

  1. 1f(−1) = 6 × (−1) + 8
  2. 2= 2

Answer2

Part (b) · 2 marks

Find an expression for g⁻¹(x), the inverse function of g(x) = (x − 1)/3.

  1. 1y = (x − 1)/3
  2. 2Swap: x = (y − 1)/3
  3. 33x = y − 1
  4. 4g⁻¹(x) = 3x + 1

Answer3x + 1

Part (c) · 3 marks

Solve the equation fg(x) = 14 for x.

  1. 1fg(x) = 6((x − 1)/3) + 8
  2. 2= 2(x − 1) + 8 = 2x + 6
  3. 32x + 6 = 14
  4. 4x = 4

Answer4

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