## Calculus (3rd Edition)

$f(x)=x^{-4/3}$ is contiuous on $(-\infty,0)\cup(0,\infty)$.
Since $x^{-4/3}$ is defined for all $x\neq 0$ then the domain of $f(x)=x^{-4/3}$ is $(-\infty,0)\cup(0,\infty)$. Now, since $x^{-4/3}$ is continous for all $x\neq 0$, then by using the continuity laws, $f(x)=x^{-4/3}$ is contiuous on $(-\infty,0)\cup(0,\infty)$.