2015 IJC P1 Q6
The function $\text{f}$ is defined by
$\text{f : }x\mapsto {{\text{e}}^{x-2}}-3,\ \ \ \text{ }x\in \mathbb{R}$.
(i)
Find ${{\text{f}}^{-1}}(x)$ and write down the domain and range of ${{\text{f}}^{-1}}$.
[3]
(ii)
Sketch on the same diagram the graphs of $y=\text{f}(x)$, $y={{\text{f}}^{-1}}(x)$ and $y=\text{f}{{\text{f}}^{-1}}(x)$, giving the equations of any asymptotes and the exact coordinates of any points where the curves cross the $x$- and $y$-axes.
[4]
(iii)
Find the area of the region bounded between $y=\text{f}(x)$ and $y={{\text{f}}^{-1}}(x)$, giving your answer correct to $2$ decimal places.
[2]
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