The real valued function


The real valued function $f(x)=\frac{\operatorname{cosec}^{-1} x}{\sqrt{x-[x]}}$, where $[\mathrm{x}]$ denotes the greatest integer less than or equal to $x$, is defined for all $x$ belonging to:

  1. (1) all reals except integers

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

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

  4. (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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