The function f(x)=3sin2πx+x−[x]+sin4πx where [x]denotes the greatest integer less than or equal to x is

We have sin2πx+sin4πx=12(1−cos2πx)+18(3−4 cos2πx+cos4πx)=78−cos2πx+18cos4πxPeriod = L.C.M of 2π2π,2π4π=1also x-[x] is periodic with period 1∴ Period = 1