Question

The domain of definition of the function $f\left(x\right)=log|x|$ is

• A. $R$
• B. $(-\infty ,0)$
• C. $(0,\infty )$
• D. $R-\left\{0\right\}$

Answer 1

The correct option is D

$R-\left\{0\right\}$

$f\left(x\right)=log|x|$
For f(x) to be defined, x > 0, which is always true.
But $x\ne 0\Rightarrow x\ne 0$
Thus, dom (f) = R - {0}