2022 ACJC P1 Q6
The function $\text{h}$ is defined by $\text{h}:x\mapsto \left| \ln \left( 2x \right) \right|+1$, $x\in \mathbb{R}$, $0<x\le \lambda $.
(i)
Find the maximum value of $\lambda $ for which the inverse function $\text{h}$ exist.
[1]
(ii)
Using $\lambda =\frac{1}{2}$,
(a) Find ${{\text{h}}^{-1}}$ and state its domain,
[4]
(b) sketch the graph of $y=\text{h}{{\text{h}}^{-1}}\left( x \right)$,
[1]
(c) find the solution set for $\text{h}\left( x \right)={{\text{h}}^{-1}}\left( x \right)$.
[1]
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