Express \(2 x ^ { 2 } - 12 x + 13\) in the form \(a ( x + b ) ^ { 2 } + c\), where \(a , b\) and \(c\) are constants.
The function f is defined by \(\mathrm { f } ( x ) = 2 x ^ { 2 } - 12 x + 13\) for \(x \geqslant k\), where \(k\) is a constant. It is given that f is a one-one function. State the smallest possible value of \(k\).
The value of \(k\) is now given to be 7 .
Find the range of f .
Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\) and state the domain of \(\mathrm { f } ^ { - 1 }\).