Answer
$ y $ is continuous on
$$(-\infty,\infty)$$
Work Step by Step
Given $$ y=\frac{1}{|x|+1}-\frac{x^2}{2}$$
Since $|x|$ is always a positive value, the denominator ($|x|+1\ne 0 \ \forall \ x\in R $ ) and $\frac{x^2}{2}$ is defined on $ R $
So, $ y $ is continuous on
$$(-\infty,\infty)$$
