Question

How do you find the x values at which `f(x)=1/(x^2+1)` is not continuous, which of the discontinuities are removable?

Answer 1

`f(x)` is continuous everywhere

Explanation:

I am assuming that `x` is real (ie `x in RR`) and we are not talking about a complex variable function (`x in CC`).

Th denominator is positive for all real numbers
(we write this as `x^2+1>0 AA x in RR`

As such `f(x)` is continuous everywhere

graph{1/(x^2+1) [-30, 30, -1.5, 1.5]}