11 The function f is defined by \(\mathrm { f } ( x ) = 10 + 6 x - x ^ { 2 }\) for \(x \in \mathbb { R }\).
- By completing the square, find the range of f .
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The function g is defined by \(\mathrm { g } ( x ) = 4 x + k\) for \(x \in \mathbb { R }\) where \(k\) is a constant. - It is given that the graph of \(y = \mathrm { g } ^ { - 1 } \mathrm { f } ( x )\) meets the graph of \(y = \mathrm { g } ( x )\) at a single point \(P\).
Determine the coordinates of \(P\).
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