2022 NJC Promo Q8
The function $\text{f}$ is defined by
$\text{f}\left( x \right)=\left\{ \begin{matrix}
x-4\,\,\,\,\,\text{for}\,\,\,\,\,x\le 1 \\
\cos x\,\,\,\,\,\text{for}\,\,\,\,\,1<x\le \pi \\
\end{matrix} \right.$
(i)
Show that $\text{f}$ has an inverse.
[3]
(ii)
Find ${{\text{f}}^{-1}}$.
[3]
(iii)
Evaluate ${{\text{f}}^{2}}\left( \frac{\pi }{2} \right)$ and find ${{\text{f}}^{2}}$.
[4]
(iv)
Find ${{\text{f}}^{2022}}\left( 0 \right)$.
[2]
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