# OCR A Level: Core 3 - Functions [January 2013 Q8]

**Algebra**Level pending

The functions \(\text{f}\) and \(\text{g}\) are defined for all real values of \(x\) by \[\text{f}(x) = x^2+4ax+a^2 \quad \text{and} \quad \text{g}(x)=4x-2a\] where \(a\) is a positive constant.

\((\text{i})\) Find the range of \(\text{f}\) in terms of \(a\).

\((\text{ii})\) Given that \(\text{fg}(3)=69\), find the value of \(a\) and hence find the value of \(x\) such that \(\text{g}^{-1}(x)=x\).

**Input \(3 \times\) the value of \(x\) from part \((\text{ii})\) as your answer.**

###### There are **4** marks available for part (i) and **6** marks for part (ii).

###### In total, this question is worth **13.9%** of all available marks in the paper.

###### This is part of the set OCR A Level Problems.

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