Let f:[-1,3]→R be defined as f(x)=|x|+[x],-1≤x<1x+|x|,1≤x<2x+[x],2≤x≤3where [t] denotes the greatest integer less than or equal to t. Then, the number of points at which f is discontinuous are

Given function is f(x)=|x|+[x],−1≤x<1x+|x|,1≤x<2x+[x],2≤x≤3=−x−1,−1≤x<0x,0≤x<12x,1≤x<2x+2,2≤x<36x=3⇒f(−1)=0,f−1+=0f0−=−1,f(0)=0,f0+=0f1−=1,f(1)=2,f1+=2f2−=4,f(2)=4,f2+=4f3−=5,f(3)=6Therefore, f(x) is discontinuous at 0,1,3Hence the number of discontinuous points of the function fx is 3