3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d8e25332-3a45-43ca-a5b8-0a16f47f13b9-08_542_540_269_696}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of part of the graph \(y = \mathrm { f } ( x )\) where
$$\mathrm { f } ( x ) = 2 | 3 - x | + 5 \quad x \geqslant 0$$
- Solve the equation
$$f ( x ) = \frac { 1 } { 2 } x + 30$$
Given that the equation \(\mathrm { f } ( x ) = k\), where \(k\) is a constant, has two distinct roots,
- state the set of possible values for \(k\).
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