4MA1/2HR Jun 2022, Question 19: Composite Functions
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
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The question, in short
Given f(x) = x² − 4 and g(x) = 2x + 1, solve the inequality fg(x) > 0, showing clear algebraic working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 1fg(x) = (2x + 1)² − 4
- 2(2x + 1)² − 4 = 4x² + 4x + 1 − 4
- 34x² + 4x − 3 > 0
- 4Solve 4x² + 4x − 3 = 0
- 5(2x + 3)(2x − 1) = 0
- 6x = −3/2 or x = 1/2
- 7Critical values: −3/2 and 1/2
- 84x² + 4x − 3 > 0 when x < −3/2 or x > 1/2
- 9x < −3/2, x > 1/2
Answerx < −3/2, x > 1/2
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