7. The function \(f\) is defined by
$$\mathrm { f } : x \rightarrow 3 \mathrm { e } ^ { x - 1 } , \quad x \in \mathbb { R }$$
- State the range of f .
- Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\) and state its domain.
The function \(g\) is defined by
$$g : x \rightarrow 5 x - 2 , \quad x \in \mathbb { R }$$
Find, in terms of e,
- the value of \(\mathrm { gf } ( \ln 2 )\),
- the solution of the equation
$$\mathrm { f } ^ { - 1 } \mathrm {~g} ( x ) = 4$$