Question

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

Answer 1

`f(x)= x/(x^2+1)` is defined and continuous in all of `RR`

Explanation:

`f(x) = x/(x^2+1)`

is a rational function, that is the quotient of two polynomials. As such it is defined and continuous everywhere except where the denominator vanishes.

However as:

`x^2 + 1 >0 AAx in RR`

We can conclude that `f(x)` is defined and continuous in all of `RR`