Express \(2 x ^ { 2 } - 12 x + 11\) in the form \(a ( x + b ) ^ { 2 } + c\), where \(a , b\) and \(c\) are constants.
The function f is defined by \(\mathrm { f } ( x ) = 2 x ^ { 2 } - 12 x + 11\) for \(x \leqslant k\).
State the largest value of the constant \(k\) for which f is a one-one function.
For this value of \(k\) find an expression for \(\mathrm { f } ^ { - 1 } ( x )\) and state the domain of \(\mathrm { f } ^ { - 1 }\).
The function g is defined by \(\mathrm { g } ( x ) = x + 3\) for \(x \leqslant p\).
With \(k\) now taking the value 1 , find the largest value of the constant \(p\) which allows the composite function fg to be formed, and find an expression for \(\mathrm { fg } ( x )\) whenever this composite function exists.
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.