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4024/12 Oct/Nov 2022, Question 21: Inverse Functions

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 6 marks

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The question, in short

Given f(x) = 1 + 3x/2 and g(x) = 2/(1 − x), find the inverse of f and solve an equation involving g and f.

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

Part (a) · 3 marks

Find f⁻¹(x), the inverse function of f.

  1. 1y = 1 + 3x/2
  2. 2Swap x and y: x = 1 + 3y/2
  3. 33y/2 = x − 1, so 3y = 2(x − 1)
  4. 4f⁻¹(x) = (2(x − 1))/3

Answer(2(x−1))/3 or (2x−2)/3

Part (b) · 3 marks

Solve g(x) = f(−4) for x.

  1. 1f(−4) = 1 + (3 × −4)/2 = 1 − 6 = −5
  2. 22/(1 − x) = −5
  3. 32 = −5(1 − x) = −5 + 5x
  4. 45x = 7, so x = 7/5

Answer7/5

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

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Also searched as: 4024/12/O/N/22 · 4024_w22_qp_12 · 4024 w22 12 · question 21.
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