- The functions \(f\) and \(g\) are defined by
$$\begin{array} { l l }
\mathrm { f } : x \mapsto \mathrm { e } ^ { - x } + 2 , & x \in \mathbb { R }
\mathrm {~g} : x \mapsto 2 \ln x , & x > 0
\end{array}$$
- Find \(\mathrm { fg } ( x )\), giving your answer in its simplest form.
- Find the exact value of \(x\) for which \(\mathrm { f } ( 2 x + 3 ) = 6\)
- Find \(\mathrm { f } ^ { - 1 }\), stating its domain.
- On the same axes, sketch the curves with equation \(y = \mathrm { f } ( x )\) and \(y = \mathrm { f } ^ { - 1 } ( x )\), giving the coordinates of all the points where the curves cross the axes.