7. \(\quad \mathrm { f } ( x ) = \frac { 2 } { x - 1 } - \frac { 6 } { ( x - 1 ) ( 2 x + 1 ) } , x > 1\)
- Prove that \(\mathrm { f } ( x ) = \frac { 4 } { 2 x + 1 }\).
- Find the range of f.
- Find \(\mathrm { f } ^ { - 1 } ( x )\).
- Find the range of \(\mathrm { f } ^ { - 1 } ( x )\).