7.
\includegraphics[max width=\textwidth, alt={}, center]{039ebdba-4ad5-4974-9345-d66712fa0a08-3_401_712_228_479} The diagram 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.

1. Showing, in terms of \(a\) and \(b\), the coordinates of any points of intersection with the axes, sketch on separate diagrams the graphs of
   1. \(y = \mathrm { f } ^ { - 1 } ( x )\),
   2. \(y = 2 \mathrm { f } ( 3 x )\). Given that $$\mathrm { f } ( x ) = 2 - \sqrt { x + 9 } , \quad x \in \mathbb { R } , \quad x \geq - 9$$
2. find the values of \(a\) and \(b\),
3. find an expression for \(\mathrm { f } ^ { - 1 } ( x )\) and state its domain.