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4024/12 Oct/Nov 2024, Question 22: 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) = (3x − 1)/2 and g(x) = 5ˣ, evaluate f at a value, find the inverse of f, and solve an equation linking f and g.

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

Part (a) · 1 mark

Calculate f(−7) using the given formula for f.

  1. 1f(−7) = (3 × (−7) − 1)/2 = −22/2
  2. 2= −11

Answer−11

Part (b) · 2 marks

Find an expression for f⁻¹(x), the inverse function of f.

  1. 1y = (3x − 1)/2
  2. 22y = 3x − 1, so 2y + 1 = 3x, x = (2y + 1)/3
  3. 3f⁻¹(x) = (2x + 1)/3

Answer(2x+1)/3

Part (c) · 3 marks

Given f(9/25) = g(x), find the value of x.

  1. 1f(9/25) = (3 × 9/25 − 1)/2 = (27/25 − 25/25)/2 = 1/25
  2. 25ˣ = 1/25 = 5⁻²
  3. 3x = −2

Answer−2

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Also searched as: 4024/12/O/N/24 · 4024_w24_qp_12 · 4024 w24 12 · question 22.
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