- The functions f and g are defined by
$$\mathrm { f } : x \mapsto \mathrm { e } ^ { x } + 2 \quad x \in \mathbb { R }$$
$$\mathrm { g } : x \mapsto \ln x \quad x > 0$$
- State the range of f .
- Find \(\mathrm { fg } ( x )\), giving \(y\) our 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.