2021 NYJC P1 Q5
(b)
The function $\text{g}$ is given by
$\text{g}:x\mapsto \ln \left( \frac{{{e}^{x}}+5}{{{e}^{x}}-1} \right)$, for $x\in \mathbb{R}$, $x>0$.
(i) Find ${{\text{g}}^{-1}}\left( x \right)$ and states its domain.
The function $\text{h}$ is defined by
$\text{h}:x\mapsto 1+\sqrt{9-{{\left( x-2 \right)}^{2}}}$, for $x\in \mathbb{R}$, $-1\le x\le 5$.
(ii) Find the exact solutions of ${{\text{g}}^{2021}}\text{h}\left( x \right)=\ln 2$, giving your answer in its simplest form.
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