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0580/22 May/Jun 2022, Question 19: Inverse Functions

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 4 marks

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The question, in short

Given f(x) = 7x − 8, g(x) = 4/x + 5 and h(x) = 2ˣ + 1, find an inverse function and solve an equation linking h and g.

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Part (a) · 2 marks

Find the inverse function f⁻¹(x) for f(x) = 7x − 8.

  1. 1y = 7x − 8, swap: x = 7y − 8
  2. 2y = (x + 8)/7
  3. 3f⁻¹(x) = (x + 8)/7

Answer(x + 8)/7

Part (b) · 2 marks

Find the value of x for which h(x) equals g(1/3).

  1. 1g(1/3) = 4 ÷ 1/3 + 5 = 12 + 5 = 17
  2. 22ˣ + 1 = 17, so 2ˣ = 16 = 2⁴
  3. 3x = 4

Answer4

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