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

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 $\text{g}^{-1}(x)=x$ .

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

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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.

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This is part of the set OCR A Level Problems .