2022 HCI J1 BT Q1
A piecewise function is given as
$\text{f}\left( x \right)=\left\{ \begin{matrix}
3-x\text{ for }1\le x\le 3, \\
\sqrt{4-{{\left( x-5 \right)}^{2}}}\text{ for }3<x\le 5 \\
\end{matrix} \right.$
And that $\text{f}\left( x \right)=\text{f}\left( x-4 \right)$ for all real values of $x$.
(i)
Find the exact values of $\text{f}\left( 8 \right)$ and $\text{f}\left( -10 \right)$.
[2]
Another function $\text{g}$ is defined as $\text{g}\left( x \right)=\ln x$, ${{e}^{2}}<x<{{e}^{4}}$.
(ii)
Show that $\text{fg}$ exists and find the exact range of $\text{fg}$.
[3]
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