2022 HCI P1 Q6
The function $\text{f}$ is defined by
$\text{f}:x\mapsto \left\{ \begin{matrix}
5+\ln x\,\,\,\,\,\,\,\text{for}\,\,0<x<1, \\
-{{x}^{2}}+6x\,\,\,\,\text{for }1\le x\le a, \\
\end{matrix} \right.$
where $a$ is a constant.
(i)
Given that $\text{f}$ has an inverse, determine the range of values of $a$.
[2]
(ii)
Given that $a$ satisfies the range of values found in part (i), sketch the graph of $\text{f}$, indicating clearly the coordinates of the end point(s) in terms of $a$.
[2]
(iii)
Find ${{\text{f}}^{-1}}$ in similar form.
[3]
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