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4024/12 May/Jun 2023, Question 17: 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) = 2 − 3x and g(x) = x − 4, find the inverse of f and solve an equation linking f and g.

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

Part (a) · 2 marks

Find f⁻¹(x) for f(x) = 2 − 3x.

  1. 1y = 2 − 3x
  2. 2Swap: x = 2 − 3y, so 3y = 2 − x
  3. 3f⁻¹(x) = (2 − x)/3

Answer(2 − x)/3

Part (b) · 3 marks

Solve f(x + 5) = 3g(x) using the given functions.

  1. 1f(x + 5) = 2 − 3(x + 5) = −3x − 13
  2. 23g(x) = 3(x − 4) = 3x − 12
  3. 3−3x − 13 = 3x − 12
  4. 4−6x = 1
  5. 5x = −1/6

Answer−1/6

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Also searched as: 4024/12/M/J/23 · 4024_s23_qp_12 · 4024 s23 12 · question 17.
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