## Calculus (3rd Edition)

$f(x)$ is continuous on $R$.
Since $x^4+1\gt 0$ for all $x\in R$, then the domain of the function $f(x)=(x^4+1)^{3/2}$ is $R$, and since $x^4+1$ is a polynomial then it is continuous. Now by using the continuity laws, $f(x)$ is continuous on $R$.