8 A function f is defined by \(\mathrm { f } ( x ) = 2 \mathrm { e } ^ { 3 x } - 1\) for all real values of \(x\).
- Find the range of f.
- Show that \(\mathrm { f } ^ { - 1 } ( x ) = \frac { 1 } { 3 } \ln \left( \frac { x + 1 } { 2 } \right)\).
- Find the gradient of the curve \(y = \mathrm { f } ^ { - 1 } ( x )\) when \(x = 0\).