Answer
$(-\infty,\infty)$
Work Step by Step
We are given the function:
$f(x)=\sqrt[3]{x^2-2x-3}$.
First determine the domain on which the function is defined:
$D=(-\infty,\infty)$
$f(x)$ is a composed function of the functions $x^2-2x-3$ and $\sqrt[3] x$. Both functions are continuous, therefore their composition is also continuous on the domain.
The interval of continuity is:
$(-\infty,\infty)$
