## Calculus (3rd Edition)

$f(x)=\frac{x^2}{x+x^{1/4}}$ is continuous on $(0,\infty)$.
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 $(0,\infty)$.