Question

Let `f(x) = (|__x__|)/(x^2 + 1)` where `|__x__|` denotes the greatest integer less than or equal to x. Then?

A. `f` is continuous for all `x`.
B. `f` is continuous only when `x` is an integer.
C. `f` is continuous only when `x` is not an integer.
D. `f` is not continuous at any value of `x`.

I know that the function is continuous at every point except at `x^2 +1 = 0`
But `x^2 = -1` is not a real number.
Please help.

Answer 1

See below.

Explanation:

Attached a function plot explaining the function behavior.