4 The functions f and g are defined by
$$\begin{array} { l l }
\mathrm { f } ( x ) = 5 - \mathrm { e } ^ { 3 x } , & \text { for all real values of } x
\mathrm {~g} ( x ) = \frac { 1 } { 2 x - 3 } , & \text { for } x \neq 1.5
\end{array}$$
- Find the range of f.
- The inverse of f is \(\mathrm { f } ^ { - 1 }\).
- Find \(\mathrm { f } ^ { - 1 } ( x )\).
- Solve the equation \(\mathrm { f } ^ { - 1 } ( x ) = 0\).
- Find an expression for \(\operatorname { gg } ( x )\), giving your answer in the form \(\frac { a x + b } { c x + d }\), where \(a , b , c\) and \(d\) are integers.
[0pt]
[3 marks]