4. The curve with equation \(y = 2 + \ln ( 4 - x )\) meets the line \(y = x\) at a single point, \(x = \beta\).
a. Show that \(2 < \beta < 3\)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{63d85737-99d4-4916-a479-fe44f77b1505-07_961_1002_296_513}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows the graph of \(y = 2 + \ln ( 4 - x )\) and the graph of \(y = x\).
A student uses the iteration formula
$$x _ { n + 1 } = 2 + \ln \left( 4 - x _ { n } \right) , \quad n \in N ,$$
in an attempt to find an approximation for \(\beta\).
Using the graph and starting with \(x _ { 1 } = 3\),
b. determine whether the or not this iteration formula can be used to find an approximation for \(\beta\), justifying your answer.