2. For the following functions \(f\) and \(g\), determine with reason whether \((fog)(x)\) exists:
(a) \(f : \mathbb{R} \to \mathbb{R}\), where \(f(x) = x^2\) and \(g : [5, \infty) \to \mathbb{R}\), with \(g(x) = -\sqrt{x - 5}\).
(b) \(f : \mathbb{R} \to \mathbb{R}\), where \(f(x) = \frac{2}{x - 4}\) and \(g : [\ln(3), \infty) \to \mathbb{R}\), with \(g(x) = e^x\).
