Answer
$ f(x)=\frac{x^2}{x+x^{1/4}}$ is continuous on $(0,\infty)$.
Work Step by Step
Putting $ x+x^{1/4}=0$, then $ x=0$ and since $ x^{1/4}$ is defined only when $ x\geq 0$ then the domain of $ f(x)=\frac{x^2}{x+x^{1/4}}$ is $(0,\infty)$. Now, since both $ x^2$ and $ x+x^{1/4}$ are continuous, then by using the continuity laws, $ f(x)=\frac{x^2}{x+x^{1/4}}$ is continuous on $(0,\infty)$.
