Answer
See the explanation
Work Step by Step
Recall: $f$ is continuous at $a$ if $\lim_{r\to a}f(r)=f(a)$.
$\lim_{r\to -2}f(r)=\lim_{r\to -2}\sqrt[3]{4r^2-2r+7}$ Use the properties of limits
$=\sqrt[3]{\lim_{r\to -2}(4r^2-2r+7)}$ Evaluate the limit by direct substitution
$=\sqrt[3]{4(-2)^2-2(-2)+7}$
$=f(-2)$
Thus, $f(r)$ is continuous at $a=-2$.
