2021 NJC Promo Q5

It is given that

\(\mathrm{f}\left( x \right)=\left\{ \begin{matrix} {{\left( x-2 \right)}^{2}},0\le x<2 \\ 2x-4,2\le x\le 4 \\ \end{matrix} \right.\)

and that \(\mathrm{f}\left( x \right)=\mathrm{f}\left( x+4 \right)\) for all real values of \(x\).

1. State the value of \(\mathrm{f}\left( 21 \right)\).[1]
2. Sketch the graph of \(y=\mathrm{f}\left( x \right)\) for \(-6\le x\le 6\).[2]

The function \(\mathrm{g}\) is defined by

\(\mathrm{g}\left( x \right)=\sqrt{x-4}\), \(4\le x\le 20\).

3. Find \(\mathrm{fg}\) in a similar form as \(\mathrm{f}\).[4]