- The function f is defined by
$$\mathrm { f } : x \mapsto \frac { 3 ( x + 1 ) } { 2 x ^ { 2 } + 7 x - 4 } - \frac { 1 } { x + 4 } , \quad x \in \mathbb { R } , x > \frac { 1 } { 2 }$$
- Show that \(\mathrm { f } ( x ) = \frac { 1 } { 2 x - 1 }\)
- Find \(\mathrm { f } ^ { - 1 } ( x )\)
- Find the domain of \(\mathrm { f } ^ { - 1 }\)
$$\mathrm { g } ( x ) = \ln ( x + 1 )$$
- Find the solution of \(\mathrm { fg } ( x ) = \frac { 1 } { 7 }\), giving your answer in terms of e .