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4024/22 Oct/Nov 2020, Question 6: Composite Functions

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 8 marks

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The question, in short

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

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

Part (a) · 1 mark

Substitute x = −5 into f(x) = 4(2 − x) and calculate the result.

  1. 1f(−5) = 4(2 − (−5)) = 4 × 7 = 28

Answer28

Part (b) · 2 marks

Solve the inequality 4(2 − x) > 3 for x.

  1. 14(2 − x) > 3, so 8 − 4x > 3
  2. 25 > 4x
  3. 3x < 5/4

Answerx < 5/4

Part (c) · 2 marks

Find the inverse function f⁻¹(x) of f(x) = 4(2 − x).

  1. 1y = 4(2 − x), so y/4 = 2 − x
  2. 2x = 2 − y/4 = (8 − y)/4
  3. 3f⁻¹(x) = (8 − x)/4

Answer(8− x)/4

Part (d) · 3 marks

Using f(p) = g(2p + 1) with the given f and g, find the value of p.

  1. 14(2 − p) = 7 − 3(2p + 1)/5
  2. 2Multiply by 5: 40 − 20p = 35 − 6p − 3
  3. 38 = 14p
  4. 4p = 8/14 = 4/7

Answer4/7

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Also searched as: 4024/22/O/N/20 · 4024_w20_qp_22 · 4024 w20 22 · question 6.
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