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 \(c\).

Solve the equation \(3x + 2 = \frac{2}{x - 1}\).

The function \(f\) is defined by \(f(x) = x^2 - 4x + 8\) for \(x \in \mathbb{R}\). Find the set of values of \(x\) for which \(f(x) < 9\), giving your answer in exact form.

A curve is described by the equation \(y = 2x^2 - 6x + 5\). Determine the range of \(x\) values for which \(y > 13\).

Find the set of values of \(x\) for which \(x^2 + 6x + 2 > 9\).

The function \(f\) is defined by \(f : x \mapsto 6x - x^2 - 5\) for \(x \in \mathbb{R}\). Find the set of values of \(x\) for which \(f(x) \leq 3\).

Find the set of values of \(x\) satisfying \(4x^2 - 12x > 7\).

A curve is defined by the equation \(y = 2x^2 - 3x\). Determine the set of \(x\) values for which \(y > 9\).

The function \(f\) is defined by \(f: x \mapsto x^2 - 3x\) for \(x \in \mathbb{R}\). Find the set of values of \(x\) for which \(f(x) > 4\).