Answer
No discontinuities
Work Step by Step
Note that $sin(x)$ is continuous for all values of $x$. Thus, the only discontinuities possible are where the input is not real.
The input to $sin(x)$ in $f(x) = sin(x^2-2)$ is $x^2-2$. This, again, produces real values for all values of $x$. Thus, there exist no discontinuities.
