If f(x)=1-4x2,  0≤x<1x22x,  1≤x<2where . denotes the greater integer function then  fxis

since 1≤x<2 or 0≤x-1<1x2−2x=x−12−1=x−12−1=0−1=−1∴fx=1−4x2    ,  0≤x<124x2−1    ,  12≤x<2−1           ,   1≤x<2 It is clear from graph that f(x) is discontinuous at x=1 and not differentiable at x=12 and x=1