10 The function \(\mathrm { f } : x \mapsto 2 x ^ { 2 } - 8 x + 14\) is defined for \(x \in \mathbb { R }\).
- Find the values of the constant \(k\) for which the line \(y + k x = 12\) is a tangent to the curve \(y = \mathrm { f } ( x )\).
- Express \(\mathrm { f } ( x )\) in the form \(a ( x + b ) ^ { 2 } + c\), where \(a , b\) and \(c\) are constants.
- Find the range of f .
The function \(\mathrm { g } : x \mapsto 2 x ^ { 2 } - 8 x + 14\) is defined for \(x \geqslant A\).
- Find the smallest value of \(A\) for which g has an inverse.
- For this value of \(A\), find an expression for \(\mathrm { g } ^ { - 1 } ( x )\) in terms of \(x\).
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