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4024/11 May/Jun 2024, Question 19: Functions as a Mapping

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 6 marks

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The question, in short

For f(x) = 2x − 5, evaluate f(11), find the inverse function f⁻¹(x), and solve f(x) = x² + x − 11.

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Part (a) · 1 mark

Work out the value of f(11) using f(x) = 2x − 5.

  1. 1f(11) = 2 × 11 − 5 = 17

Answer17

Part (b) · 2 marks

Find an expression for the inverse function f⁻¹(x).

  1. 1y = 2x − 5
  2. 2Swap: x = 2y − 5, so y = (x + 5)/2
  3. 3f⁻¹(x) = (x + 5)/2

Answer(x + 5)/2

Part (c) · 3 marks

Solve the equation 2x − 5 = x² + x − 11 for x.

  1. 12x − 5 = x² + x − 11
  2. 2x² − x − 6 = 0
  3. 3(x − 3)(x + 2) = 0
  4. 4x = 3 or x = −2

Answer3 or −2

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Also searched as: 4024/11/M/J/24 · 4024_s24_qp_11 · 4024 s24 11 · question 19.
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