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4024/21 Oct/Nov 2022, Question 4: Composite Functions

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 9 marks

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The question, in short

Given f(x) = x² − 7 and g(x) = (4 − 3x)/2, evaluate f(8), evaluate g(−2), find the inverse g⁻¹(x), and solve f(2x − 1) + 3 = 0.

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

Part (a) · 1 mark

Substitute x = 8 into f(x) = x² − 7 and work out the value.

  1. 1f(8) = 8² − 7 = 64 − 7 = 57

Answer57

Part (b) · 1 mark

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

  1. 1g(−2) = (4 − 3 × −2)/2 = (4 + 6)/2 = 5

Answer5

Part (c) · 3 marks

Rearrange g(x) = (4 − 3x)/2 to make x the subject and state g⁻¹(x).

  1. 1y = (4 − 3x)/2
  2. 2Swap: x = (4 − 3y)/2
  3. 32x = 4 − 3y, so 3y = 4 − 2x
  4. 4g⁻¹(x) = (4 − 2x)/3

Answer(4 − 2x)/3

Part (d) · 4 marks

Form an equation from f(2x − 1) + 3 = 0 using x² − 7, then solve for x.

  1. 1(2x − 1)² − 7 + 3 = 0
  2. 2(2x − 1)² = 4
  3. 32x − 1 = ±2, so 2x = 1 ± 2
  4. 4x = −1/2 and x = 3/2

Answer−1/2 and 3/2

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Also searched as: 4024/21/O/N/22 · 4024_w22_qp_21 · 4024 w22 21 · question 4.
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