If [x] represents the greatest integer functi | vedclass

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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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