Let f:[-1,2] R be given by f(x)=2 x^2+x+ [x^2 ]-[x] , where [t] denotes the greatest integer less than or equal to t . The number of points, where f is not continuous, is :

Step-by-step solution

Doubtful points : -1,0,1, 2 , 3 , 2 at x= 2 , 3 ( array cc f(x)= (2 x^2+x-[x] )+ [x^2 ]= Discount Cont. Cont. array ) at x=-1 : . array rl RHL & f(x)=(2-1-(-1))+0=2 & f(-1)=2-1-(-1)+1=3 array Dis. at x=2 : . array rl LHL f(x) & =8+2-1+3=12 f(2) & =8+2-2+4=12 array Cont. at x =0 : . array rl LHL & 0+0-(-1)+0=1 & f (0)=0 array Dis. at x =1 . array rl LHL & 2+1-0+0=3 & f(1)=3-1+1=3 RHL & 2+1-1+1=3 array Cont.