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0580/22 Oct/Nov 2021, Question 20: Composite Functions

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 5 marks

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The question, in short

Given f(x) = 2ˣ⁻³, g(x) = 2x − 1 and h(x) = 5/(x − 4), evaluate composite expressions and solve an equation linking f and h.

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

Part (a) · 2 marks

Calculate ff(6), applying f twice starting with input 6.

  1. 1f(6) = 2⁶⁻³ = 2³ = 8
  2. 2ff(6) = f(8) = 2⁸⁻³ = 2⁵ = 32

Answer32

Part (b) · 1 mark

Find g⁻¹g(x + 21), simplifying the result.

  1. 1g⁻¹ undoes g, so g⁻¹g(x + 21) = x + 21

Answerx + 21

Part (c) · 2 marks

Solve f(x) = h(84) for x.

  1. 1h(84) = 5/(84 − 4) = 5/80 = 1/16 = 2⁻⁴
  2. 22ˣ⁻³ = 2⁻⁴, so x − 3 = −4
  3. 3x = −1

Answer−1

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Also searched as: 0580/22/O/N/21 · 0580_w21_qp_22 · 0580 w21 22 · question 20.
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