Answer
$f(x)$ is continuous over the interval $(-\infty, -2)$ U $(-2, \infty).$
Work Step by Step
$f(x)=\dfrac{4x^2+7x-2}{x+2}=\dfrac{(4x-1)(x+2)}{(x+2)}=4x-1;x\ne-2.$
The only restriction on $f(x)$'s domain is that $x\ne-2,$ hence the function is continuous over the interval $(-\infty, -2)$ U $(-2, \infty).$
