Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2012  OctNov  (P19709/13)  Q#6
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Question
The functions and are defined for by
Solve the following equations for .
i. , giving your answer in terms of .
ii. , giving your answers correct to 2 decimal places.
Solution
i.
We have the functions;
We write as;
We are given that;
Therefore;
ii.
We have the functions;
We write as;
We are given that;
Therefore;
We utilize the symmetry property of to find other solutions (roots) of :


Symmetry 

Hence;
For ;
Therefore, all the solutions of within are;
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