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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:

(i) Graph shown; (ii) x < a or x > a + 1/√b