# 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.

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