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(A) The function is defined as $f(x) = \sqrt{\frac{[x]-x}{x-[x]}}$.For any $x \in R$, let $x = [x] + \{x\}$, where $0 \leq \{x\} < 1$.Then $x - [x] =

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$\phi$

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(A) The function is defined as $f(x) = \sqrt{\frac{[x]-x}{x-[x]}}$.For any $x \in R$, let $x = [x] + \{x\}$, where $0 \leq \{x\} Then $x - [x] = \{x\}$.If $x 
otin Z$, then $\{x\} 
eq 0$, so we can write the expression as:$f(x) = \sqrt{\frac{-\{x\}}{\{x\}}} = \sqrt{-1} = i$.Since $i$ is not a real number, $f(x)$ is not real for any $x 
otin Z$.If $x \in Z$, then $[x] = x$, which makes the denominator $x - [x] = 0$.Division by zero is undefined, so $f(x)$ is not defined for $x \in Z$.Therefore, there are no real values of $x$ for which $f(x)$ is real.The set of such values is the empty set, denoted by $\phi$.

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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