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4024/21 Oct/Nov 2020, Question 10: Inverse Functions

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 7 marks

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The question, in short

Given f(x) = (3 − 2x)/5 and g(x) = (x − 7)/4, evaluate f at −4, find the inverse of f, and solve g(p) = f(p + 1) for p.

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Part (a) · 1 mark

Substitute x = −4 into f(x) = (3 − 2x)/5 and work out the value.

  1. 1f(−4) = (3 − 2 × (−4))/5 = 11/5 = 2.2

Answer2.2

Part (b) · 3 marks

Find the inverse function f⁻¹(x) for f(x) = (3 − 2x)/5.

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

Answer(3−5x)/2

Part (c) · 3 marks

Using g(p) = f(p + 1), form an equation in p and find the value of p.

  1. 1(p − 7)/4 = (3 − 2(p + 1))/5 = (1 − 2p)/5
  2. 25(p − 7) = 4(1 − 2p), so 5p − 35 = 4 − 8p
  3. 313p = 39, p = 3

Answer3

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