how do i prove this $S=\{(x,y,z): x^2 +4y^2 +4 z^2 -2x +16y +40z +113 <0\}$ is an open set

Question

Elipsoide in the three-dimensional space, with the graph of the ellipsoid the set is open, but how do I prove it?

Answer 1

If $f(x,y,z)$ is a polynomial of three variables, then $f$ is continuous. Since $f$ is continuous, what can we say about $f^{-1}(U)$ when $U\subset\Bbb R$ is open?