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4024/12 May/Jun 2024, Question 20: Inverse 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 − 4x)/5, find the inverse function and simplify the difference between f(x) and f(2x).

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Part (a) · 3 marks

Find f⁻¹(x) for f(x) = (2 − 4x)/5.

  1. 1y = (2 − 4x)/5
  2. 25y = 2 − 4x
  3. 34x = 2 − 5y, so x = (2 − 5y)/4
  4. 4f⁻¹(x) = (2 − 5x)/4

Answer(2 − 5x)/4

Part (b) · 2 marks

Simplify f(x) − f(2x) using the given function.

  1. 1f(2x) = (2 − 8x)/5
  2. 2f(x) − f(2x) = (2 − 4x − 2 + 8x)/5
  3. 3= 4x/5

Answer(4x)/5

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Also searched as: 4024/12/M/J/24 · 4024_s24_qp_12 · 4024 s24 12 · question 20.
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