Question

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

• A. $(-\infty ,1)\cup (1,\infty )$
• B. $(-\infty ,1)$
• C. $(0,1)\cup (1,\infty )$
• D. $(1,\infty )$

Answer 1

The correct option is C $(0,1)\cup (1,\infty )$

We have,
$f\left(x\right)=\log |\log x|$

$f\left(x\right)$ is defined when
$|\log x|>0$ and $x>0$
$\Rightarrow x\ne 1$ and $x>0$
$\Rightarrow x\in (0,1)\cup (1,\infty )$

Hence, domain of the function $f\left(x\right)$ is $(0,1)\cup (1,\infty ).$