1. (6 marks) For $f(x) = \frac{1}{x^2 - 4}$ and $g(x) = \sqrt{x - 1}$, determine the subset of the domain of $g$ on which the composition $f \circ g$ is well-defined, and then determine the subset of the domain of $f$ on which the composition $g \circ f$ is well-defined. In other words, determine the domains of $f \circ g$ and $g \circ f$. Then, find formulas for $(f \circ g)(x)$ and $(g \circ f)(x)$.
