Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/12) | Q#2

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Question

The functions  and  are defined for  by


where  and  are constants. Given that  and , find

     i.       the values of  and ,

   ii.       an expression for .

Solution


i.
 

We are given that;

We need to find  and . First we find ;

We have;

For ;

Now we evaluate ;

We are given that;

Therefore;

Now we find the .

We have;

To find the inverse of a given function  we need to write it in terms of  rather than in terms of .

Interchanging ‘x’ with ‘y’;

Now we evaluate ;

We are given that;

Therefore;


ii.
 

We have the functions;

Substituting values of  and  from (i) we get;

For ;

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