Question

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

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

Answer 1

Answer: (C)

$x^2-\left[x^2\right]=\left\{x^2\right\}>0 ;$ but $0 \leq\{y\}<1 \Rightarrow\left\{x^2\right\} \neq 0 \Rightarrow x \neq \pm \sqrt{n}$