3 The functions \(f\) and \(g\) are defined with their respective domains by
$$\begin{array} { l l }
\mathrm { f } ( x ) = 3 - x ^ { 2 } , & \text { for all real values of } x
\mathrm {~g} ( x ) = \frac { 2 } { x + 1 } , & \text { for real values of } x , x \neq - 1
\end{array}$$
- Find the range of f.
- The inverse of g is \(\mathrm { g } ^ { - 1 }\).
- Find \(\mathrm { g } ^ { - 1 } ( x )\).
- State the range of \(\mathrm { g } ^ { - 1 }\).
- The composite function gf is denoted by h .
- Find \(\mathrm { h } ( x )\), simplifying your answer.
- State the greatest possible domain of h .