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Question Number 185574 by mnjuly1970 last updated on 23/Jan/23

$$$$$$f\left(x\right)=cos\left(2\pi x\right)+sin\left(2\pi x\right)+\sqrt{\lfloor x\rfloor +\lfloor -x\rfloor }$$$$$$$$find{R}_f=?$$

Commented by mahdipoor last updated on 23/Jan/23

$$\sqrt{\left[x\right]+[-x]}=\{\begin{array}{l}0x\in Z\\ \sqrt{-1}=ix\notin Z\end{array}$$$$\Rightarrow D_f=Z\Rightarrow f\left(x\right)=cos\left(2\pi k\right)+sin\left(2\pi k\right)+0=1$$

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