2021 ACJC P1 Q3
The function $\text{f}$ is defined as $\text{f}:x\mapsto \frac{a}{2-x}$, $x\in \mathbb{R}$, $x\ne 0,2$.
(i)
Find ${{\text{f}}^{2}}$ and ${{\text{f}}^{-1}}$ in terms of $a$, stating their domains clearly.
[5]
(ii)
Find the value of $a$ such that ${{\text{f}}^{2}}\left( x \right)={{\text{f}}^{-1}}\left( x \right)$ for all $x\in \mathbb{R}$, $x\ne 0,2,\frac{a}{2}$.
[2]
(iii)
Using the value of $a$ found in (ii), find ${{\text{f}}^{2021}}\left( x \right)$.
[2]
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