Simple question

Draw the graph and analyse the given condition

Now take any integral value and try to make LHS and RHS limits eqaul

taking 1 we get

Lim(1+) =1=LHS

Lim(1-)=0=RHS

We are getting that LHS is not eqaul to RHS

this shows it will not continuous

similarly if we take any integral value we will always get LHS not equal to x

so,from this we can say

[x] will be continuous at all value of x except integers