Question

Question 19: Show that the function defined by is discontinuous at all integral point. Here denotes the greatest integer less than or equal to x.

Class 12 - Math - Continuity and Differentiability

Answer 1

Here g(x) = x-[x]
let f(x) = x and q(x) = [x]
Now f(x) being an identity function is continuous for all real x
and q(x) = [x] bring greatest integer function is discontinuous at every integer value of x .
also f(x) -q(x) = g(x)

Hence g(x) = x-[x] is discontinuous for all integral values of x .