2017 NJC Promo Q7
The functions $\text{f}$ and $\text{g}$ are defined as
$\text{f}:x\mapsto \frac{3x}{2x-5},$ for $-5<x\le 5$, $x\ne \frac{5}{2}$
$\text{g}\left( x \right)=\left\{ \begin{matrix}
8x-{{x}^{2}}-15,\text{ for }3\le x<4. \\
\frac{5-x}{2},\text{ for }4\le x<6. \\
\end{matrix} \right.$
(i)
Find ${{\text{f}}^{-1}}$, stating its domain and range.
[4]
(ii)
Find the value of $\text{g}\left( 4 \right)$.
[1]
(iii)
Sketch the graph of $y=\text{g}\left( x \right)$.
[2]
(iv)
Show that the composite function $\text{fg}$ exists and find the range of $\text{fg}$.
[3]
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