The real valued function


The real valued function $f(\mathrm{x})=\frac{\operatorname{cosec}^{-1} \mathrm{x}}{\sqrt{\mathrm{x}-[\mathrm{x}]}}$, where

$[\mathrm{x}]$ denotes the greatest integer less than or equal to $\mathrm{x}$, is defined for all $\mathrm{x}$ belonging to :


  1. all reals except integers

  2. all non-integers except the interval $[-1,1]$

  3. all integers except $0,-1,1$

  4. all reals except the Interval $[-1,1]$

Correct Option: , 2


$f(x)=\frac{\operatorname{cosec}^{-1} x}{\sqrt{\{x\}}}$

Domain $\in(-\infty,-1] \cup[1, \infty)$

$\{x\} \neq 0$ so $x \neq$ integers


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