4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5b698944-41ac-4072-b5e1-c580b7752c39-10_606_613_285_278}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5b698944-41ac-4072-b5e1-c580b7752c39-10_602_608_287_1062}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 1 shows a sketch of part of the graph \(y = \mathrm { f } ( x )\), where
$$f ( x ) = 2 | 3 - x | + 5 , \quad x \geqslant 0$$
Figure 2 shows a sketch of part of the graph \(y = \mathrm { g } ( x )\), where
$$\operatorname { g } ( x ) = \frac { x + 9 } { 2 x + 3 } , \quad x \geqslant 0$$
- Find the value of \(\mathrm { fg } ( 1 )\)
- State the range of g
- Find \(\mathrm { g } ^ { - 1 } ( x )\) and state its domain.
Given that the equation \(\mathrm { f } ( x ) = k\), where \(k\) is a constant, has exactly two roots,
- state the range of possible values of \(k\).