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Question
Write the domain of the real function
`f (x) = sqrt([x] - x) .`
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Solution
[x] is the greatest integer function.
\[\left[ x \right] \leq x, \forall x \in R\]
\[ \Rightarrow \left[ x \right] - x \leq 0, \forall x \in R\]
\[ \Rightarrow \sqrt{\left[ x \right] - x} \text{ does not exist for anyx} \in R . \]
\[\text{Domain} =\phi\]
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