Express \(3 x ^ { 2 } - 12 x + 14\) in the form \(3 ( x + a ) ^ { 2 } + b\), where \(a\) and \(b\) are constants to be found.
The function \(\mathrm { f } ( x ) = 3 x ^ { 2 } - 12 x + 14\) is defined for \(x \geqslant k\), where \(k\) is a constant.
Find the least value of \(k\) for which the function \(\mathrm { f } ^ { - 1 }\) exists.
For the rest of this question, you should assume that \(k\) has the value found in part (b).
Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).
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Hence or otherwise solve the equation \(\mathrm { ff } ( x ) = 29\).