5. The functions \(f\) and \(g\) are defined by
$$\begin{array} { l l }
\mathrm { f } : x \mapsto \ln ( 2 x - 1 ) , & x \in \mathbb { R } , x > \frac { 1 } { 2 }
\mathrm {~g} : x \mapsto \frac { 2 } { x - 3 } , & x \in \mathbb { R } , x \neq 3
\end{array}$$
- Find the exact value of fg(4).
- Find the inverse function \(\mathrm { f } ^ { - 1 } ( x )\), stating its domain.
- Sketch the graph of \(y = | \mathrm { g } ( x ) |\). Indicate clearly the equation of the vertical asymptote and the coordinates of the point at which the graph crosses the \(y\)-axis.
- Find the exact values of \(x\) for which \(\left| \frac { 2 } { x - 3 } \right| = 3\).