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4024/12 Oct/Nov 2025, Question 20: Composite Functions

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

Given f(x) = ax + 3 and g(x) = (x + b)², find the inverse of f, then use gf(x) = 9x² + 24x + 16 with positive integers a and b to find a and b.

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Part (a) · 2 marks

Find f⁻¹(x) for f(x) = ax + 3.

  1. 1y = ax + 3, swap: x = ay + 3
  2. 2ay = x − 3
  3. 3f⁻¹(x) = (x − 3)/a

Answer(x−3)/a

Part (b) · 3 marks

Given gf(x) = 9x² + 24x + 16 and a, b positive integers, find the values of a and b.

  1. 1gf(x) = (ax + 3 + b)²
  2. 29x² + 24x + 16 = (3x + 4)²
  3. 3a = 3 and 3 + b = 4
  4. 4a = 3, b = 1

Answera = 3, b = 1

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Also searched as: 4024/12/O/N/25 · 4024_w25_qp_12 · 4024 w25 12 · question 20.
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