Mathematics

The quotient function $(f/g)(x)$ is really just division, and division has one non-negotiable rule: you can't divide by zero. So the key insight is that $(f/g)(x) = \frac{f(x)}{g(x)}$ exists only when the denominator is non-zero at that point. This single condition determines the entire domain of the quotient.

The quotient function $(f/g)(x)$ is really just division, and division has one non-negotiable rule: you can't divide by zero. So the key insight is that $(f/g)(x) = \frac{f(x)}{g(x)}$ exists only when the denominator is non-zero at that point. This single condition determines the entire domain of the quotient.