3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f0a633e3-5c63-4d21-8ffa-d4e7dc43a536-06_476_1107_221_422}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of part of the graph of \(y = \mathrm { g } ( x )\), where
$$g ( x ) = 3 + \sqrt { x + 2 } , \quad x \geqslant - 2$$
- State the range of g .
- Find \(\mathrm { g } ^ { - 1 } ( x )\) and state its domain.
- Find the exact value of \(x\) for which
$$\mathrm { g } ( x ) = x$$
- Hence state the value of \(a\) for which
$$\mathrm { g } ( a ) = \mathrm { g } ^ { - 1 } ( a )$$