Answer
$ f(x)=x^{1/3}+x^{3/4} $ is contiuous on $[0,\infty)$
Work Step by Step
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 $[0,\infty)$.
