Inferior goods, monotonic utility and strict concavity
I could not add images in the comments, therefore I used this method.

I think that the convexity definition does not hold for the function, since there are pairs of points that when they are conected, produce a segment which are out of the set. Because of it, the set is not convex.

Here there is an example of such situation with this function, which does not show a convex set: