5. \(\mathrm { f } ( x ) = 5 + \mathrm { e } ^ { 2 x - 3 } , x \in \mathbb { R }\).
- State the range of f .
- Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\) and state its domain.
- Solve the equation \(\mathrm { f } ( x ) = 7\).
- Find an equation for the tangent to the curve \(y = \mathrm { f } ( x )\) at the point where \(y = 7\).