Question

write the points of discontinuity for the function f(x)=[x],-3<x<3​

Answer 1

✪ᴀɴsᴡᴇʀ✪

• Discontinuous at - 2, - 1, 0, 1, 2.

★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★

$\:\:\: f(x) = [x], - 3 < x < 3$

Let $n \in (-3,3), n \in Z$

$\:\:\: f(x) = n-1, n-1 ≤ x < n$

$\:\:\: f(x) = n, n ≤ x < n+1$

From the above analysis it is clear that

$\lim \limits_{x \to n^-} f(x) = n-1$

$\lim \limits_{x \to n^+} f(x) = n$

So,$LHL ≠ RHL$ at all integral points. Hence f(x) is discontinuous at all integral points i.e. - 2, - 1, 0, 1, 2.