## Calculus (3rd Edition)

$f(x)=x^{1/3}+x^{3/4}$ is contiuous on $[0,\infty)$
Since $x^{1/3}$ is defined for all $x\in R$ and $x^{3/4}$ is defined only on $[0,\infty)$, then the domain of $f(x)=x^{1/3}+x^{3/4}$ is $[0,\infty)$. Now, since $x^{1/3}$ and $x^{3/4}$ are continuous, then by using the continuity laws $f(x)=x^{1/3}+x^{3/4}$ is contiuous on $[0,\infty)$.