2015 VJC P1 Q4
The function $\text{g}$ is defined by
$\text{g}:x\mapsto {{e}^{x}}-7x,x>\lambda $,
where $\lambda $ is a real constant.
(i)
Find the exact minimum value of $\lambda $ such that the inverse of $\text{g}$ exists.
[2]
Using the value of $\lambda $ found in (i),
(ii)
find ${{\text{g}}^{-1}}\left( 1 \right)$,
[2]
(iii)
sketch the graphs of $y=\text{g}\left( x \right)$, $y={{\text{g}}^{-1}}\left( x \right)$ and $y=\text{g}{{\text{g}}^{-1}}\left( x \right)$ on a single diagram.
[3]
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