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

Algebra Level 3

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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