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Problem 364
364
The function \(f\) is defined for \(x \in \mathbb{R}\) by \(f(x) = x^2 - 6x + c\), where \(c\) is a constant. It is given that \(f(x) > 2\) for all values of \(x\). Find the set of possible values of \(c\).
Solution
Given the function \(f(x) = x^2 - 6x + c\), we need \(f(x) > 2\) for all \(x\).