Do you know its property ?-8

Algebra Level 5

Which of the following functions are periodic?

a.   sgn(ex)\large a. ~~~\text{sgn}\left(e^{-x}\right)

b.   sinx+sinx\large b.~~~|\sin x| +\sin x

c.   min(4cosx,x)\large c.~~~\min(4\cos x,|x|)

d.   x+12+x12+2x\large d.~~~\left\lfloor x+\dfrac{1}{2}\right\rfloor +\left\lfloor x-\dfrac{1}{2}\right\rfloor +2\lfloor -x\rfloor

Details and Assumptions:

  • \lfloor\cdot\rfloor represents the Floor Function.

  • sgn(x)\text{sgn}(x) represents the sign function. We have sgn(x)=1,0,1\text{sgn}(x)=-1,0,1 for negative, zero, positive xx respectively.

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