7 Functions f and g are defined by
$$\begin{aligned}
& \mathrm { f } : x \mapsto \frac { 3 } { 2 x + 1 } \quad \text { for } x > 0
& \mathrm {~g} : x \mapsto \frac { 1 } { x } + 2 \quad \text { for } x > 0
\end{aligned}$$
- Find the range of f and the range of g .
- Find an expression for \(\mathrm { fg } ( x )\), giving your answer in the form \(\frac { a x } { b x + c }\), where \(a , b\) and \(c\) are integers.
- Find an expression for \(( \mathrm { fg } ) ^ { - 1 } ( x )\), giving your answer in the same form as for part (ii).