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Tim Gan Math

2017 A-Level H2 Mathematics

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Question 2Inequalities6 marks
  1. On the same axes, sketch the graphs of \(y=\frac{1}{x-a}\) and \(y=b\left| x-a \right|\), where \(a\) and \(b\) are positive constants.[2]
  2. Hence, or otherwise, solve the inequality \(\frac{1}{x-a} < b\left| x-a \right|\).[4]
Solution step 1, image 1
Solution step 2, image 1

Final Answer:

(ii) ${x < a}$ or ${x > a + \sqrt{\frac{1}{b}}}$