Question

The domain of $f\left(x\right)={\cot }^{-1}\left(\frac{x}{\sqrt{x^2-\left[x^2\right]}}\right)$ is
( $[.]$ denotes the greatest integer function)

• A. $(0,\infty )$
• B. $R-\left\{0\right\}$
• C. $R-\{x:x\in Z\}$
• D. $(-\infty ,0)$

Answer 1

The correct option is C $R-\{x:x\in Z\}$

$f\left(x\right)={\cot }^{-1}\left(\frac{x}{\sqrt{x^2-\left[x^2\right]}}\right)$
For $f\left(x\right)$ to be defined, $x^2-\left[x^2\right]>0$
$\therefore x^2$ should not be an integer
Hence, $x$ should not be an integer.
Hence, Option C is the answer