Q41 / 160 · TS EAMCET 2022 (20 Jul Shift 2) · Mathematics

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

  • Correct answer
    A
    $\phi$
  • B
    $\mathbb{R}$
  • C
    $\mathbb{Z}$
  • D
    $\mathbb{R}-\mathbb{Z}$

Solution

$f(x)=\sqrt{\frac{[x]-x}{x-[x]}}=\sqrt{\frac{-\{x-[x]\}}{x-[x]}}=\sqrt{-1}=i$ $$ \Rightarrow \mathrm{f}(\mathrm{x})=\mathrm{i} \forall \mathrm{x} \leftarrow \mathbb{R} $$ $\Rightarrow \nexists$ any $\mathrm{x} \leftarrow \mathrm{R}$ s.t $\mathrm{f}(\mathrm{x}) \leftarrow \mathbb{R}$.

Hence, the correct answer is option: 'A'.

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