The real-valued function f(x) = frac{operator | vedclass

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(B) For the function $f(x) = \frac{\operatorname{cosec}^{-1} x}{\sqrt{x - [x]}}$ to be defined,two conditions must be satisfied:$1$. The domain of $\o

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

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(B) For the function $f(x) = \frac{\operatorname{cosec}^{-1} x}{\sqrt{x - [x]}}$ to be defined,two conditions must be satisfied:$1$. The domain of $\operatorname{cosec}^{-1} x$ is $(-\infty, -1] \cup [1, \infty)$.$2$. The denominator $\sqrt{x - [x]}$ must be non-zero and real. Since $x - [x] = \{x\}$ (the fractional part of $x$),we require $\{x\} > 0$,which means $x$ cannot be an integer.Combining these conditions,$x$ must be in $(-\infty, -1] \cup [1, \infty)$ and $x 
otin \mathbb{Z}$.This corresponds to all non-integers in the set $(-\infty, -1] \cup [1, \infty)$,which is equivalent to all non-integers except the interval $(-1, 1)$.

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

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