Question

If $f\left(x\right)={\tan }^{-1}\left(\log \right(|x|)$, then the set of values of Range $-$ Domain is

• A. $\left\{0\right\}$
• B. $\varphi$
• C. $(-\frac{\pi }{2},\frac{\pi }{2})-\left\{0\right\}$
• D. $R-(-\frac{\pi }{2},\frac{\pi }{2})$

Answer 1

The correct option is A

$\left\{0\right\}$

$f\left(x\right)={\tan }^{-1}\left(\log \right(|x|)$
$x\ne 0\Rightarrow$ Domain $=R-\left\{0\right\}$

We know that, $\log |x|\in R$
$\Rightarrow$ Range of $f\left(x\right)=(-\frac{\pi }{2},\frac{\pi }{2})$

$\therefore$ Range$-$Domain $=\left\{0\right\}$