7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a36989df-555f-4727-b6c6-e66362380011-4_481_808_248_424}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the graph of \(y = \mathrm { f } ( x )\) which meets the coordinate axes at the points \(( a , 0 )\) and \(( 0 , b )\), where \(a\) and \(b\) are constants.
- Showing, in terms of \(a\) and \(b\), the coordinates of any points of intersection with the axes, sketch on separate diagrams the graphs of
- \(\quad y = \mathrm { f } ^ { - 1 } ( x )\),
- \(y = 2 \mathrm { f } ( 3 x )\).
Given that
$$\mathrm { f } ( x ) = 2 - \sqrt { x + 9 } , \quad x \in \mathbb { R } , \quad x \geq - 9 ,$$
- find the values of \(a\) and \(b\),
- find an expression for \(\mathrm { f } ^ { - 1 } ( x )\) and state its domain.