Proving f cannot be convex

Question

The following question I encountered in a convex optimization course and I can't seem to understand the solution.

Answer 1

I think the answer provided means that when the function is restricted to the line (I) it is not convex. So the function $f$ is not convex.

Answer 2

from the picture of level set, it shows function looks like the shape of $x^2 + y^2$, so it is convex (downward)