Let x be the greatest integer less than or equals to x .Then, at which of the following points(S) the functions fx=x cos πx+x is discontinuous?

fx=xcos πx+xf(0+)= 0 cos π0+0=0 and f0-=0 cosπ0-1=0  therefore f0+=f0-=f0 , hence fx is continuous at x=0f(1−)=1cosπ=−1f(1+)=1cos(2π)=1 dis continuousf(2−)=2cos3π=-2f(2+)=2cos4π=2f(2)=2cos4π=2dis continuousf(−1+)=−1cos2π=−1f(−1−)=−1cos3π=1dis continuous