<ol class="abc-list" start="2"><li><div class="list-item-content"><span class="list-item-text">The function $\mathrm{g}$ is given by</span></div><div class="list-item-paragraph" style="text-align: center">$\mathrm{g}:x\mapsto \ln \left( \frac{{{e}^{x}}+5}{{{e}^{x}}-1} \right)$, for $x\in \mathbb{R}$, $x>0$.</div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find ${{\mathrm{g}}^{-1}}\left( x \right)$ and states its domain.</span></div><div class="list-item-paragraph">The function $\mathrm{h}$ is defined by</div><div class="list-item-paragraph" style="text-align: center">$\mathrm{h}:x\mapsto 1+\sqrt{9-{{\left( x-2 \right)}^{2}}}$, for $x\in \mathbb{R}$, $-1\le x\le 5$.</div></li><li><div class="list-item-content"><span class="list-item-text">Find the exact solutions of ${{\mathrm{g}}^{2021}}\mathrm{h}\left( x \right)=\ln 2$, giving your answer in its simplest form.</span></div></li></ol></li></ol>

$\mathrm{g}:x\mapsto \ln \left( \frac{{{e}^{x}}+5}{{{e}^{x}}-1} \right)$, for $x\in \mathbb{R}$, $x>0$.

Find ${{\mathrm{g}}^{-1}}\left( x \right)$ and states its domain.

Find the exact solutions of ${{\mathrm{g}}^{2021}}\mathrm{h}\left( x \right)=\ln 2$, giving your answer in its simplest form.

2021 NYJC P1 Q5

2021 NYJC P1 Q5

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