Lemmara logoLemmaraWorked solution

4MA1/2H Jun 2020, Question 21: Inverse Functions

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

For f(x) = 5 + 6x − x² with x ≤ 3, rewrite the quadratic in completed-square form and then determine when the inverse function gives positive values.

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

Part (a) · 2 marks

Write 5 + 6x − x² as p − (x − q)², stating the constants p and q.

  1. 15 + 6x − x² = 5 − (x² − 6x)
  2. 2x² − 6x = (x − 3)² − 9
  3. 3So 5 − ((x − 3)² − 9) = 5 + 9 − (x − 3)²
  4. 4= 14 − (x − 3)²

Answer14 − (x − 3)²

Part (b) · 5 marks

Use the completed-square form to find the x values making f⁻¹(x) positive.

  1. 1y = 14 − (x − 3)², so (x − 3)² = 14 − y
  2. 2x ≤ 3, so take the negative root: x = 3 − √(14 − y)
  3. 3f⁻¹(x) = 3 − √(14 − x), defined for x ≤ 14
  4. 4f⁻¹(x) > 0: √(14 − x) < 3, so 14 − x < 9, x > 5
  5. 55 < x ≤ 14

Answer5 < x ≤ 14

Stuck on a step? Read the free lesson: Inverse Functions

Practise more inverse functions questions

Real 4MA1 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 inverse functions

Also searched as: 4MA1 2H June 2020 · 4MA1/2H · 4ma1 jun20 2h · question 21.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.