Answer
See details below.
Work Step by Step
We are given the function $ f(x)=\frac{1}{x^2+1}$. Since $ f(x)$ is a quotient of polynomials, and $1+x^2$ can not be zero for any $ x\in R $, then by Theorem 2 the function
$$ f(x)=\frac{1}{x^2+1}$$
is continuous.
