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0580/22 Oct/Nov 2022, Question 17: Composite Functions

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 6 marks

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The question, in short

Given f(x) = x², g(x) = (x + 5)/2 and h(x) = 7x − 3, evaluate f(−3), find the inverse of g, and solve gf(x) = hh⁻¹(63) for x > 0.

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Part (a) · 1 mark

Work out the value of f(−3) using f(x) = x².

  1. 1f(−3) = (−3)² = 9

Answer9

Part (b) · 2 marks

Find an expression for g⁻¹(x), the inverse function of g(x) = (x + 5)/2.

  1. 1y = (x + 5)/2
  2. 22y = x + 5
  3. 3x = 2y − 5
  4. 4g⁻¹(x) = 2x − 5

Answer2x − 5

Part (c) · 3 marks

Solve gf(x) = hh⁻¹(63) for x > 0, using the three given functions.

  1. 1gf(x) = (x² + 5)/2
  2. 2hh⁻¹(63) = 63
  3. 3(x² + 5)/2 = 63
  4. 4x² + 5 = 126, so x² = 121
  5. 5x = 11 (x > 0)

Answer11

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Also searched as: 0580/22/O/N/22 · 0580_w22_qp_22 · 0580 w22 22 · question 17.
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