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4024/12 Oct/Nov 2021, Question 24: Composite Functions

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 6 marks

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The question, in short

Given f(x) = 2x² + 7x + 4 and g(x) = 2x + 6, evaluate f(3), find the inverse of g, and solve f(x) − g(x) = 1.

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Part (ai) · 1 mark

Calculate the value of f(3).

  1. 1f(3) = 2 × 9 + 7 × 3 + 4 = 18 + 21 + 4 = 43

Answer43

Part (aii) · 2 marks

Find an expression for g⁻¹(x).

  1. 1y = 2x + 6 → y − 6 = 2x → x = (y − 6)/2
  2. 2g⁻¹(x) = (x − 6)/2

Answer(x −6)/2

Part (b) · 3 marks

Solve the equation f(x) − g(x) = 1 for x.

  1. 12x² + 7x + 4 − (2x + 6) = 1
  2. 22x² + 5x − 3 = 0
  3. 3(2x − 1)(x + 3) = 0
  4. 4x = 1/2 or x = −3

Answer1/2 and −3

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Also searched as: 4024/12/O/N/21 · 4024_w21_qp_12 · 4024 w21 12 · question 24.
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