Question

Domain of the function $f(x)=\frac{1}{\sqrt{\ln {\cot }^{-1}x}}$ is

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

Answer 1

Answer: (D)

$\ln \left({\cot }^{-1}x\right)>0$
${\cot }^{-1}x>1$
$x<\cot 1$
$\therefore \text{ domain }(-\infty ,\cot 1)$