2015 PJC P2 Q1
The function $\text{f}$ is defined by
$\text{f}:x\mapsto \lambda x-{{x}^{2}},\quad x\in \mathbb{R},\quad x>\frac{\lambda }{2},$
where $\lambda >2$.
(i)
Find, in terms of $\lambda $, ${{\text{f}}^{-1}}\left( x \right)$, stating the domain of ${{\text{f}}^{-1}}$.
[4]
(ii)
On the same diagram, sketch the graphs of $y=\text{f}\left( x \right)$ and $y={{\text{f}}^{-1}}\left( x \right)$, showing their graphical relationship clearly.
[2]
(iii)
Find, in terms of $\lambda $, the solution of the equation $\text{f}\left( x \right)={{\text{f}}^{-1}}\left( x \right)$.
[3]
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