Answer
domain: $(-\infty, 0) \cup (0, +\infty)$
Work Step by Step
RECALL:
The logarithmic function $f(x) = \log_a{x}$ is defined only when $x \gt 0$. Thus, its domain is $x \gt 0$.
This means that the function $f(x) = \log_2{(x^2)}$ is defined only when $x^2 \gt 0$.
Note that the value of $x^2$ will always be greater than zero except when $x=0$. This means that the given function is undefined only when $x=0$.
Thus, the domain of the given function is the set of all real numbers except 0.
In interval notation, the domain is $(-\infty, 0) \cup (0, +\infty)$.
