$\large f(x)=\frac{2x(\sin (x)+ \tan( x))}{2\left \lfloor 2+\frac{x}{\pi} \right \rfloor -3}$

For all real $x$ , which of these answer choices is the property of $f(x)$ ?

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This is a tricky problem.

It is given that $f(x) = \dfrac {2x(\sin{x}+\tan{x})}{2 \lfloor 2+\frac{x}{\pi}\rfloor -3} = \dfrac {g(x)}{h(x)}$

We note that:

Therefore, $\boxed{f(x) \text{ is an odd function}}$ .

This is how it looks like. Isn't it odd?!!!