2006 MJC Promo
The function $\text{f}$ is defined by
$\text{f}:x\mapsto \ln \left( {{x}^{2}}-x-2 \right)$, $c<x<d$, where $c<d<0$.
(a)
Find the values of $c$ and $d$ such that the range of $\text{f}$ consists of all real values which are less than $\text{e}$.
(b)
Find an expression for ${{\text{f}}^{-1}}\left( x \right)$ for all the values of $c$ and $d$ found in (a).
(c)
Write down an expression for $\text{h}\left( x \right)$ such that $\text{hf}\left( x \right)={{x}^{2}}-x-2$.
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