We have to check which of the following of the above is the convex set. I tried this problem by taking the level curve of $f(x,y)$ at $c$ and plotted it and then for $y=c$, I checked all those points on $x$ axis such that $f(x,y)\geq c$ and from the definition of the convexity of a set I found that it is a convex set . Therefore $U$ is the convex set.
Is my approach correct? Is there any other way to look at this problem ?