Question

The number of point(s) of discontinuity of $f\left(x\right)=\left[2\cos x\right],x\in [0,2\pi ]$,is (where $[.]$ represents Greatest Integer function)

Answer 1

Graph of $2\cos x:$

Graph of $\left[2\cos x\right]:$

So, from above graph of $\left[2\cos x\right]$
$f\left(x\right)$ is discontinuous at $\{0,\frac{\pi }{3},\frac{\pi }{2},\frac{2\pi }{3},\frac{4\pi }{3},\frac{3\pi }{2},\frac{5\pi }{3},2\pi \}$
So, there are $8$ points of discontinuity.