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If $[x]$ represents the greatest integer function, then the set of all real values of $x$ for which $f(x)=\sqrt{\frac{[x]-x}{x-[x]}}$ is real is
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The correct answer is:
$\phi$
$f(x)=\sqrt{\frac{[x]-x}{x-[x]}}=\sqrt{\frac{-\{x-[x]\}}{x-[x]}}=\sqrt{-1}=i$
$$
\Rightarrow \mathrm{f}(\mathrm{x})=\mathrm{i} \forall \mathrm{x} \leftarrow \mathbb{R}
$$
$\Rightarrow \nexists$ any $\mathrm{x} \leftarrow \mathrm{R}$ s.t $\mathrm{f}(\mathrm{x}) \leftarrow \mathbb{R}$.
$$
\Rightarrow \mathrm{f}(\mathrm{x})=\mathrm{i} \forall \mathrm{x} \leftarrow \mathbb{R}
$$
$\Rightarrow \nexists$ any $\mathrm{x} \leftarrow \mathrm{R}$ s.t $\mathrm{f}(\mathrm{x}) \leftarrow \mathbb{R}$.
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