2021 NJC Promo Q5
It is given that
$\text{f}\left( x \right)=\left\{ \begin{matrix}
{{\left( x-2 \right)}^{2}},0\le x<2 \\
2x-4,2\le x\le 4 \\
\end{matrix} \right.$
and that $\text{f}\left( x \right)=\text{f}\left( x+4 \right)$ for all real values of $x$.
(i)
State the value of $\text{f}\left( 21 \right)$.
[1]
(ii)
Sketch the graph of $y=\text{f}\left( x \right)$ for $-6\le x\le 6$.
[2]
The function $\text{g}$ is defined by
$\text{g}\left( x \right)=\sqrt{x-4}$, $4\le x\le 20$.
(iii)
Find $\text{fg}$ in a similar form as $\text{f}$.
[4]
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