Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/12) | Q#1

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Question

Functions f and g are defined by

 ,

 ,

Solve the equation .

Solution

First we find .

We have;

We write it as;

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 find .

We have;

We write it as;

Therefore;

We are given that;

Hence;

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