9 The function f : \(x \mapsto 2 x - a\), where \(a\) is a constant, is defined for all real \(x\).
- In the case where \(a = 3\), solve the equation \(\mathrm { ff } ( x ) = 11\).
The function \(\mathrm { g } : x \mapsto x ^ { 2 } - 6 x\) is defined for all real \(x\).
- Find the value of \(a\) for which the equation \(\mathrm { f } ( x ) = \mathrm { g } ( x )\) has exactly one real solution.
The function \(\mathrm { h } : x \mapsto x ^ { 2 } - 6 x\) is defined for the domain \(x \geqslant 3\).
- Express \(x ^ { 2 } - 6 x\) in the form \(( x - p ) ^ { 2 } - q\), where \(p\) and \(q\) are constants.
- Find an expression for \(\mathrm { h } ^ { - 1 } ( x )\) and state the domain of \(\mathrm { h } ^ { - 1 }\).