Write the domain of the real function

Question:

Write the domain of the real function $f(x)=\sqrt{x-[x]}$.

Solution:

$[\mathrm{x}]$ is the greatest integral function.

So, $0 \leq x-[x]<1$

$\Rightarrow \sqrt{x-[x]}$ exists for every $x \in R$.

$\Rightarrow$ Domain $=R$

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