- It is given that
$$\begin{gathered}
\mathrm { f } ( x ) = \mathrm { e } ^ { - 2 x } \quad x \in \mathbb { R }
\mathrm {~g} ( x ) = \frac { x } { x - 3 } \quad x > 3
\end{gathered}$$
- Sketch the graph of \(y = \mathrm { f } ( x )\), showing the coordinates of any points where the graph crosses the axes.
- Find the range of g
- Find \(\mathrm { g } ^ { - 1 } ( x )\), stating the domain of \(\mathrm { g } ^ { - 1 }\)
- Using algebra, find the exact value of \(x\) for which \(\operatorname { fg } ( x ) = 3\)