Let $f(x) = \frac{1}{x}$ and $g(x) = \frac{1}{x - 1}$. What is the set of all points at which $f \circ g$ is continuous?

Explanation

1. 01

   $f(g(x))$ needs $g(x)$ to be defined, so $x \ne 1$, and $g(x) \ne 0$, which always holds.

2. 02

   On that domain $f(g(x)) = x - 1$, a polynomial, so $f \circ g$ is continuous on $\mathbb{R} - \{1\}$.