#### Answer

$F(x)$ is continuous on $(-\infty,\infty)$

#### Work Step by Step

$F(x)=\frac{2x^2-x-1}{x^2+1}$
1) Find the domain of $F(x)$
We notice that $x^2+1\gt0$ for $\forall x\in R$
So, $x^2+1\ne0$ for $\forall x\in R$
Therefore, $\frac{2x^2-x-1}{x^2+1}$ is defined for $\forall x\in R$
In other words, the domain of $F(x)$ is $(-\infty,\infty)$
2) Since $F(x)$ is a rational function, according to Theorem 5, $F(x)$ is continuous on its domain.
Therefore, $F(x)$ is continuous on $(-\infty,\infty)$