# 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

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**Question**

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.

**Solution**

i.

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 ;

**ii.
**

We are required to find the set of values of for which;

We are given that;

Therefore;

As demonstrated in (i);

Hence;

Hence;

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