suppose $ f: \mathbb{R} \rightarrow \mathbb{R}$ is M-measurable, Let E be the set of points at which f is continuous, show that E is M-measurable.

Question

I know that if f is M-measurable, that for any open set U, $f^{-1} (U)$ is M-measurable, so I tried to show the value of the set is union of open sets but then I realized that is not true for example $f(x) = x^2$ when x is rational, 0 otherwise, then the set only contains 0. And I saw a similar questions The set of points at which a real function is continuous is borel?, but here I have o show $S_p$ is M-measurable instead of open, and I could not figure out how to do that.