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0580/43 May/Jun 2026, Question 18: Solving Linear Equations

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 8 marks

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The question, in short

Given f(x) = 3x + 1 and g(x) = 5 − 3x, solve for x where they are equal, find the inverse of g, form gg(x) in simplest form, and with h(x) = 2²ˣ find x when h⁻¹(x) = 2.

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Part (ai) · 2 marks

Find the value of x for which f(x) equals g(x).

  1. 13x + 1 = 5 − 3x
  2. 26x = 4
  3. 3x = 2/3

Answer2/3

Part (aii) · 2 marks

Find the inverse function g⁻¹(x).

  1. 1y = 5 − 3x
  2. 2Swap: x = 5 − 3y
  3. 33y = 5 − x
  4. 4g⁻¹(x) = (5 − x)/3

Answer(5 − x)/3

Part (aiii) · 2 marks

Find gg(x), giving the result in its simplest form.

  1. 1gg(x) = g(5 − 3x)
  2. 2= 5 − 3(5 − 3x)
  3. 3= 5 − 15 + 9x
  4. 4= 9x − 10

Answer9x − 10

Part (b) · 2 marks

With h(x) = 2²ˣ, find x such that h⁻¹(x) = 2.

  1. 1h⁻¹(x) = 2 means x = h(2)
  2. 2h(2) = 2^(2×2) = 2⁴
  3. 3x = 16

Answer16

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Also searched as: 0580/43/M/J/26 · 0580_s26_qp_43 · 0580 s26 43 · question 18.
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