9. \begin{figure}[h] \end{figure} Figure 3 shows a sketch of the curve with equation \(y = \mathrm { f } ( x ) , x \geq 0\). The curve meets the coordinate axes at the points \(( 0 , c )\) and \(( d , 0 )\). In separate diagrams sketch the curve with equation

1. \(y = \mathrm { f } ^ { - 1 } ( x )\),
2. \(y = 3 \mathrm { f } ( 2 x )\).
   (3) Indicate clearly on each sketch the coordinates, in terms of \(c\) or \(d\), of any point where the curve meets the coordinate axes. Given that f is defined by $$\mathrm { f } : x \mapsto 3 \left( 2 ^ { - x } \right) - 1 , x \in \mathbb { R } , x \geq 0 ,$$
3. state
   1. the value of \(c\),
   2. the range of \(f\).
4. Find the value of \(d\), giving your answer to 3 decimal places. The function g is defined by $$\mathrm { g } : x \mapsto \log _ { 2 } x , x \in \mathbb { R } , x \geq 1 .$$
5. Find \(\mathrm { fg } ( x )\), giving your answer in its simplest form.