Inferior goods, monotonic utility and strict concavity Is it possible to have an inferior good under the assumption of a utility function which is strictly monotonically increasing and strictly quasiconvex?

I do not think so, but I could not find a formal proof.

*My underlying idea is that whit an inferior good, there exist a point where the utility consuming less of one good is better and then its derivative negative at that point, moreove, I think that this behaviour would break the concavity shape.
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: