9. (i) Find the exact solutions to the equations
- \(\ln ( 3 x - 7 ) = 5\)
- \(3 ^ { x } \mathrm { e } ^ { 7 x + 2 } = 15\)
(ii) The functions f and g are defined by
$$\begin{array} { l l }
\mathrm { f } ( x ) = \mathrm { e } ^ { 2 x } + 3 , & x \in \mathbb { R }
\mathrm {~g} ( x ) = \ln ( x - 1 ) , & x \in \mathbb { R } , x > 1
\end{array}$$ - Find \(\mathrm { f } ^ { - 1 }\) and state its domain.
- Find fg and state its range.