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0580/23 May/Jun 2022, Question 19: Inverse Functions

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 7 marks

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The question, in short

Given four functions f, g, h and j, find the constant k from an equation, form a composite function, and simplify an inverse plus function expression.

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

Part (a) · 2 marks

Using f(x) = kx² and f(−5k) = 675, find the value of k.

  1. 1k(−5k)² = 675
  2. 225k³ = 675, so k³ = 27
  3. 3k = 3

Answer3

Part (b) · 1 mark

Find the composite function gh(x) for g(x) = 1/x and h(x) = (7x − 2)/5.

  1. 1gh(x) = g((7x − 2)/5) = 1 ÷ (7x − 2)/5
  2. 2= 5/(7x − 2)

Answer5/(7x − 2)

Part (c) · 4 marks

Find h⁻¹(x) + j(x) and give the result in its simplest form.

  1. 1y = (7x − 2)/5 → swap: x = (7y − 2)/5, so 5x = 7y − 2
  2. 2h⁻¹(x) = (5x + 2)/7 = (10x + 4)/14
  3. 3h⁻¹(x) + j(x) = (10x + 4)/14 + (3 − 10x)/14 = 7/14
  4. 4= 1/2

Answer1/2 or 0.5

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