Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/13) | Q#3

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Question

The function  is defined for . Given that  and  find

     i.       the values of  and ,

   ii.       the range of .

  iii.       the exact value of .

Solution


i.
 

We have the function;

We are given that;

Since

Since

Subtracting both equation;

Substituting  in anyone of the above equations will yield value of . We choose;


ii.
 

We have the function;

Substituting values of  and  we get;

We know that;

Substituting extreme values of  in the given function;

Therefore range of  is given by;


iii.
 

We have the function;

Substituting values of  and  we get;

Now, for ;

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