F (x) = (x ^ 3-x) / sin π x, how many discontinuous points can we find

F (x) = (x ^ 3-x) / sin π x, how many discontinuous points can we find

Make every point whose denominator is 0 a breakpoint
That is, all the points of sin π x = 0 are
That is, x = k, K is any integer
It's all discontinuities
There are obviously countless