8 The functions \(f\) and \(g\) are defined with their respective domains by
$$\begin{array} { l l }
\mathrm { f } ( x ) = x ^ { 2 } & \text { for all real values of } x
\mathrm {~g} ( x ) = \frac { 1 } { x + 2 } & \text { for real values of } x , x \neq - 2
\end{array}$$
- State the range of f.
- Find fg(x).
- Solve the equation \(\operatorname { fg } ( x ) = 4\).
- Explain why the function f does not have an inverse.
- The inverse of g is \(\mathrm { g } ^ { - 1 }\). Find \(\mathrm { g } ^ { - 1 } ( x )\).