Lemmara logoLemmaraWorked solution

0580/41 May/Jun 2023, Question 10: Functions as a Mapping

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 9 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Using f(x) = x − 4, g(x) = 2x + 5 and h(x) = 3ˣ, evaluate, invert and combine these functions, then solve an equation linking h, g and f.

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

Part (ai) · 1 mark

Calculate the value of f at x = −3.

  1. 1f(−3) = −3 − 4 = −7

Answer−7

Part (aii) · 2 marks

Find the inverse function of g, giving it in terms of x.

  1. 1y = 2x + 5, swap x and y: x = 2y + 5
  2. 22y = x − 5
  3. 3g⁻¹(x) = (x − 5)/2

Answer(x − 5)/2

Part (aiii) · 4 marks

Expand and simplify the product f(x) × g(x) × f(x).

  1. 1f(x) × g(x) × f(x) = (x − 4)(2x + 5)(x − 4)
  2. 2(x − 4)(x − 4) = x² − 8x + 16
  3. 3(x² − 8x + 16)(2x + 5) = 2x³ + 5x² − 16x² − 40x + 32x + 80
  4. 4= 2x³ − 11x² − 8x + 80

Answer2x³ − 11x² − 8x + 80

Part (b) · 2 marks

Find x such that h(x) equals g evaluated at f(2).

  1. 1f(2) = 2 − 4 = −2
  2. 2g(−2) = 2 × (−2) + 5 = 1
  3. 33ˣ = 1 = 3⁰
  4. 4x = 0

Answer0

Stuck on a step? Read the free lesson: Functions as a Mapping

Practise more functions as a mapping questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on functions as a mapping

Also searched as: 0580/41/M/J/23 · 0580_s23_qp_41 · 0580 s23 41 · question 10.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.