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0580/42 Feb/Mar 2024, Question 11: Composite Functions

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 10 marks

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The question, in short

Given f(x) = 1/x, g(x) = 3x − 5 and h(x) = 2ˣ, find composite and inverse values, simplify an expression, and solve equations involving these functions.

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

Part (ai) · 2 marks

Find the value of gf(2).

  1. 1f(2) = 1/2
  2. 2g(1/2) = 3 × 1/2 − 5 = −3.5

Answer−3.5

Part (aii) · 2 marks

Find g⁻¹(x).

  1. 1y = 3x − 5
  2. 2y + 5 = 3x, so x = (y + 5)/3
  3. 3g⁻¹(x) = (x + 5)/3

Answer(x + 5)/3

Part (b) · 2 marks

Find g(x − 2) in its simplest form.

  1. 1g(x − 2) = 3(x − 2) − 5
  2. 2= 3x − 6 − 5 = 3x − 11

Answer3x −11

Part (ci) · 2 marks

Find the value of x for which fg(x) = 0.1.

  1. 1fg(x) = 1/(3x − 5) = 0.1
  2. 23x − 5 = 10
  3. 3x = 5

Answer5

Part (cii) · 2 marks

Find the value of x for which h(x) − g(7) = 0.

  1. 1g(7) = 3 × 7 − 5 = 16
  2. 22ˣ − 16 = 0, so 2ˣ = 16 = 2⁴
  3. 3x = 4

Answer4

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