Question

1. what is the domain of the parent reciprocal function, $f(x) = \frac{1}{x}$? $(-\infty, 0) \cap (0, \infty)$ $(-\infty, 0) \cup (0, \infty)$ $(-\infty, 0)$ $(0, \infty)$

Explanation:

Step1: Identify undefined value

The function $f(x)=\frac{1}{x}$ is undefined when $x=0$ (division by zero is invalid).

Step2: Determine valid x-values

All real numbers except 0: negative reals $(-\infty,0)$ and positive reals $(0,\infty)$. Combine with union $\cup$.

Answer:

$(-\infty,0)\cup(0,\infty)$