Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/13) | Q#1
The function f is defined by for .
i. Express in the form of .
ii. Hence find the set of values of for which , giving your answer in exact form.
We have the expression;
We use method of “completing square” to obtain the desired form. We complete the square for the terms which involve .
We have the algebraic formula;
For the given case we can compare the given terms with the formula as below;
Therefore, we can deduce that;
Hence, we can write;
To complete the square, we can add and subtract the deduced value of ;
We are required to find the set of values of for which;
We are given that;
As demonstrated in (i);