Question

Find the domain of the following function:

$f\left(x\right)={\cot }^{-1}\left(\frac{x}{\sqrt{x^2-\left[x^2\right]}}\right),x\in R$ is

• A. $R-\{\pm \sqrt{n},n\in N\}$
• B. $R-\{\sqrt{n},n\ge 0,n\in I\}$
• C. $R$
• D. $R-0$

Answer 1

Answer: (B)

$R-\{\sqrt{n},n\ge 0,n\in I\}$

Domain of ${\cot }^{-1}x$ is $R$ and $\frac{x}{\sqrt{x^2-\left[x^2\right]}}$ is defined if
$x^2\ne \left[x^2\right](\because x^2\ge \left[x^2\right])$
$\Rightarrow x^2\ne 0$ or +ve integer.
Hence domain $=R-\{\sqrt{n}:n\ge 0,n\in Z\}$