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4024/11 Oct/Nov 2023, Question 22: Composite Functions

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 6 marks

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The question, in short

Given f(x) = x/4 + 3 and g(x) = 2(x − 1), evaluate f(−8), find the inverse function f⁻¹(x), and solve f(p) = g(p + 5) for p.

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Part (a) · 1 mark

Work out the value of f(−8) using the given rule for f.

  1. 1f(−8) = −8/4 + 3 = −2 + 3 = 1

Answer1

Part (b) · 2 marks

Determine the inverse function f⁻¹(x) in terms of x.

  1. 1y = x/4 + 3; swap: x = y/4 + 3
  2. 2y/4 = x − 3, so f⁻¹(x) = 4(x − 3)

Answer4(x − 3) or 4x − 12

Part (c) · 3 marks

Using f(p) = g(p + 5), find the numerical value of p.

  1. 1p/4 + 3 = 2(p + 5 − 1) = 2p + 8
  2. 2p + 12 = 8p + 32
  3. 3−7p = 20
  4. 4p = −20/7

Answer−20/7

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Also searched as: 4024/11/O/N/23 · 4024_w23_qp_11 · 4024 w23 11 · question 22.
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