Two functions f and g are defined by \(f : x \to 3x - 1\) and \(g : x \to 2x^{3}\), evaluate \(fg(-2)\).
Given that \(\frac{1}{8^{2y - 3y}} = 2^{y + 2}\).
Given that \((\sqrt{3} - 5\sqrt{2})(\sqrt{3} + \sqrt{2}) = p + q\sqrt{6}\), find q.
If \(f(x) = \frac{1}{2 - x}, x \neq 2\), find \(f^{-1}(-\frac{1}{2})\).
Find the coefficient of \(x^{4}\) in the binomial expansion of \((1 - 2x)^{6}\).
