3. The function \(f\) is defined by
$$f : x \rightarrow \frac { 5 x + 1 } { x ^ { 2 } + x - 2 } - \frac { 3 } { x + 2 } , x > 1$$
- Show that \(\mathrm { f } ( x ) = \frac { 2 } { x - 1 } , x > 1\).
- Find \(\mathrm { f } ^ { - 1 } ( x )\).
The function \(g\) is defined by
$$\mathrm { g } : x \rightarrow x ^ { 2 } + 5 , \quad x \in \mathbb { R }$$
- Solve \(\operatorname { fg } ( x ) = \frac { 1 } { 4 }\).