If f: R R is defined by f(x)=x-[x] , where [x] is the greatest integer not exceeding x , then the set of discontinuous of f is

Step-by-step solution

We know that, f(x)= array cc x-(n-1) & for -1 < x < n 0 & for x=n x-n & for n < x < n+1 array . where n z Now, we check the continuity at x=n aligned f(n-0) & = _ x n⁻ [x-(n-1)] & = _ h 0 [n-h-n+1) & =1 f(n+0) & = _ x n⁺ [x-n] & = _ h 0 (n+h-n)=0 aligned and f(n)=0 f(x) is discontinuous at x=n Set of discontinuous of f is z