Question

The domain of $f\left(x\right)=\frac{1}{\log \left|x\right|}$ is

• A. $R-\left\{0\right\}$
• B. $R-\{0,1\}$
• C. $R-\{-1,0,1\}$
• D. $(-\infty ,\infty )$

Answer 1

The correct option is C $R-\{-1,0,1\}$

For $f$ to be defined,
$\left|x\right|>0$
$\left|x\right|\ne 1$ as $\left|\log 1\right|=0$
$\therefore x\notin \{-1,0,1\}$
$\therefore x\in R-\{-1,0,1\}$