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Algebra Level pending

Find the domain of the real-valued function \(f(x)=\dfrac{1}{\sqrt{x^2-\lfloor x \rfloor ^2}}\), where \(\lfloor \cdot \rfloor\) represents the greatest integer function.

\[\begin{array}{ll} (a)~\mathbb R - \mathbb Z &&&&&(b)~\mathbb R^+ - \mathbb Z\\ (c)~\mathbb Z &&&&&(d)~\mathbb R^+ \end{array} \]

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