10 Functions \(f\) and \(g\) are defined by
$$\begin{aligned}
& \mathrm { f } : x \mapsto 2 x - 3 , \quad x \in \mathbb { R } ,
& \mathrm {~g} : x \mapsto x ^ { 2 } + 4 x , \quad x \in \mathbb { R } .
\end{aligned}$$
- Solve the equation \(\mathrm { ff } ( x ) = 11\).
- Find the range of g .
- Find the set of values of \(x\) for which \(\mathrm { g } ( x ) > 12\).
- Find the value of the constant \(p\) for which the equation \(\mathrm { gf } ( x ) = p\) has two equal roots.
Function h is defined by \(\mathrm { h } : x \mapsto x ^ { 2 } + 4 x\) for \(x \geqslant k\), and it is given that h has an inverse.
- State the smallest possible value of \(k\).
- Find an expression for \(\mathrm { h } ^ { - 1 } ( x )\).