Answer
$ y $ is continuous on
$$(-\infty,\infty)$$
Work Step by Step
Given $$ y=\frac{\sqrt{x^4+1}}{1+\sin^2 x}$$
Since $\sqrt{x^4+1} \neq 0 \ \ \forall x \in R $, and $1+\sin^2 x \neq 0 \ \ \forall x \in R $,
So, $ y $ is continuous on
$$(-\infty,\infty)$$
