Prove that the greatest integer function defined by `f(x) = [x], 0 < x < 3` is not differentiable at `x = 1 and x = 2`.

Prove theat the greatest interger function defined by f(x)= [x], 0 lt x lt 3 is not differentiable at x=1 and x= 2.

Prove theat the greatest interger function defined by f(x)= |x|, 0 lt x lt 3 is not differentiable at x=1 and x= 2.

Prove theat the greatest interger function defined by f(x)= |x|, 0 lt x lt 3 is not differentiable at x=1 and x= 2.

Prove that the greatest interger function defined by f(x)=[x],0ltxlt3 is not differentiable at x=1 .

Prove that the greatest integer function f : R to R defined by f(x) = [x] , where [x] indicates the greatest integer not greater than x, is neither one-one nor onto.

Consider the greatest integer function, defined by f(x) =[x],0 le x lt 2 . Then,

Find all the points of discontinuity of the greatest integer function defined by f(x) = [x] , where [x] denotes the greatest integer less than or equal to x.