<p>The function $\mathrm{f}$ is defined by</p>
<p style="text-align: center">$\mathrm{f : }x\mapsto {{\mathrm{e}}^{x-2}}-3,\ \ \ \mathrm{ }x\in \mathbb{R}$.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find ${{\mathrm{f}}^{-1}}(x)$ and write down the domain and range of ${{\mathrm{f}}^{-1}}$.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">Sketch on the same diagram the graphs of $y=\mathrm{f}(x)$, $y={{\mathrm{f}}^{-1}}(x)$ and $y=\mathrm{f}{{\mathrm{f}}^{-1}}(x)$, giving the equations of any asymptotes and the exact coordinates of any points where the curves cross the $x$- and $y$-axes.</span></div><p style="text-align: right;">[4]</p></li><li><div class="list-item-content"><span class="list-item-text">Find the area of the region bounded between $y=\mathrm{f}(x)$ and $y={{\mathrm{f}}^{-1}}(x)$, giving your answer correct to $2$ decimal places.</span></div><p style="text-align: right;">[2]</p></li></ol>

$\mathrm{f : }x\mapsto {{\mathrm{e}}^{x-2}}-3,\ \ \ \mathrm{ }x\in \mathbb{R}$.

Find ${{\mathrm{f}}^{-1}}(x)$ and write down the domain and range of ${{\mathrm{f}}^{-1}}$.

Sketch on the same diagram the graphs of $y=\mathrm{f}(x)$, $y={{\mathrm{f}}^{-1}}(x)$ and $y=\mathrm{f}{{\mathrm{f}}^{-1}}(x)$, giving the equations of any asymptotes and the exact coordinates of any points where the curves cross the $x$- and $y$-axes.

Find the area of the region bounded between $y=\mathrm{f}(x)$ and $y={{\mathrm{f}}^{-1}}(x)$, giving your answer correct to $2$ decimal places.

2015 IJC P1 Q6

2015 IJC P1 Q6

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