11 The functions \(f\) and \(g\) are defined by
$$\begin{array} { l l }
f ( x ) = x ^ { 2 } + 3 & \text { for } x > 0
g ( x ) = 2 x + 1 & \text { for } x > - \frac { 1 } { 2 }
\end{array}$$
- Find an expression for \(\mathrm { fg } ( x )\).
- Find an expression for \(( \mathrm { fg } ) ^ { - 1 } ( x )\) and state the domain of \(( \mathrm { fg } ) ^ { - 1 }\).
- Solve the equation \(\mathrm { fg } ( x ) - 3 = \mathrm { gf } ( x )\).