2016 JJC Promo Q7
The functions $\text{f}$ and $\text{g}$ are defined by
$\begin{matrix}
& \text{f}:x\mapsto \left| x-2 \right|,x\in \mathbb{R} \\
& \text{g}:x\mapsto {{x}^{2}}-x,x\in \mathbb{R},x\le 0 \\
\end{matrix}$
(i)
By considering the graphs of $\text{f}$ and $\text{g}$, solve exactly the inequality of $\text{f}(x)>\text{g}(x)$.
[4]
(ii)
Explain why the composite function $\text{fg}$ exists.
[2]
(iii)
Find $\text{fg}(x)$, giving the domain of $\text{fg}$.
[2]
(iv)
Show by means of a graphical argument that ${{(\text{fg})}^{-1}}$ does not exist.
[2]
(v)
If the domain of $\text{fg}$ is restricted to $x\le a$, state the greatest value of $a$ for ${{(\text{fg})}^{-1}}$to exist. With the domain, find ${{(\text{fg})}^{-1}}(x)$.
[4]
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