TS EAMCET · Maths · Functions
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
- A \(\phi\)
- B \(\mathbb{R}\)
- C \(\mathbb{Z}\)
- D \(\mathbb{R}-\mathbb{Z}\)
Answer & Solution
Correct Answer
(A) \(\phi\)
Step-by-step Solution
Detailed explanation
\(f(x)=\sqrt{\frac{[x]-x}{x-[x]}}=\sqrt{\frac{-\{x-[x]\}}{x-[x]}}=\sqrt{-1}=i\) \[ \Rightarrow \mathrm{f}(\mathrm{x})=\mathrm{i} \forall \mathrm{x} \leftarrow \mathbb{R} \] \(\Rightarrow \nexists\) any \(\mathrm{x} \leftarrow \mathrm{R}\) s.t…
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