Question

The domain of the function $f\left(x\right)=\frac{arccotX}{\sqrt{X^2-\left[X^2\right]}}$, where [X] denotes the greatest integer not greater than x, is :

• A. $R$
• B. $R-\left\{0\right\}$
• C. $R-\{\pm \sqrt{n}:n\in 1^{+}\cup \{0\left\}\right\}$
• D. $R-\{n:n\in 1\}$

Answer 1

The correct option is D $R-\{n:n\in 1\}$

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

The real value of $x$ is always greater than or equal to greater integer function. But as integer function $x^2$ will get equal to $\left[x^2\right].$

Hence $X\in R\{n:n\in 1\}.$