Question

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

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

Answer 1

The correct option is D $(-\infty ,\cot 1)$

Given, $f\left(x\right)=\frac{1}{\sqrt{\ln {\cot }^{-1}x}}$
$\ln {\cot }^{-1}x>0$

$\Rightarrow {\cot }^{-1}x>e^0$

$\Rightarrow {\cot }^{-1}x>1$

$\Rightarrow x<\cot 1$

Hence,the domain is $(-\infty ,\cot 1)$