4MA1/1HR Jun 2018, Question 20: Composite Functions
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Two functions f and g are given for x > 0. With h defined as the composite fg, find an expression for the inverse function h⁻¹.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 1h = f(g(x)) = f((x + 1)/2) = 1 + 1/((x + 1)/2)
- 2= 1 + 2/(x + 1)
- 3Let y = 1 + 2/(x + 1)
- 4y − 1 = 2/(x + 1)
- 5x + 1 = 2/(y − 1)
- 6x = 2/(y − 1) − 1
- 7h⁻¹ : x ↦ 2/(x − 1) − 1
Answerh⁻¹ : x ↦ 2/(x − 1) − 1
Stuck on a step? Read the free lesson: Composite Functions
Practise more composite functions questions
Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on composite functions
Also searched as: 4MA1 1HR June 2018 · 4MA1/1HR · 4ma1 jun18 1hr · question 20.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.