<p>The function $\mathrm{f}$ is defined by</p>
<p style="text-align: center">$\mathrm{f}:x\mapsto -\ln (x-2)$, $x\in \mathbb{R}$, $2 < x\le 3$.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Find ${{\mathrm{f}}^{-1}}(x)$ and state the domain and range of ${{\mathrm{f}}^{-1}}$.</div><p style="text-align: right;">[4]</p></li><li><div class="list-item-paragraph">Sketch on the same diagram the graphs of $y=\mathrm{f}(x)$, $y={{\mathrm{f}}^{-1}}(x)$ and $y={{\mathrm{f}}^{-1}}\mathrm{f}(x)$, giving the equations of any asymptotes and the exact coordinates of any points where the curves cross the $x$- and $y$- axes.</div><p style="text-align: right;">[6]</p></li><li><div class="list-item-paragraph">Explain why the x-coordinate of the point of intersection of the graph of $y=\mathrm{f}(x)$ and $y={{\mathrm{f}}^{-1}}(x)$ satisfies the equation</div><div class="list-item-paragraph" style="text-align: center">$x+\ln (x-2)=0$,</div><div class="list-item-paragraph">and find the value of this $x$-coordinate.</div><p style="text-align: right;">[2]</p></li></ol>

$\mathrm{f}:x\mapsto -\ln (x-2)$, $x\in \mathbb{R}$, $2 < x\le 3$.

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

Explain why the x-coordinate of the point of intersection of the graph of $y=\mathrm{f}(x)$ and $y={{\mathrm{f}}^{-1}}(x)$ satisfies the equation

and find the value of this $x$-coordinate.

Modulus Functions

Functions

H2 Math

International Baccalaureate Higher Level Mathematics

2020 TMJC Promo Q7

2020 TMJC Promo Q7

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