The given function f(x)=[x] is discontinuous at :

The correct answer is option (1) → every integer

for every integer x

$[x]=x$

$\lim\limits_{y→x^+}[y]=x$ but $\lim\limits_{y→x^-}[y]=x-1$

so $LHL≠RHL$

[x] is discontinuous at every integer