Question: Determine whether

(a) Reciprocals of positive concave functions are convex

(b) Reciprocals of positive convex functions are concave

(c) There exists a convex function \(f:{{\mathbb{R}}_{++}}\to \mathbb{R}\) such that \(f\left( x \right)\le \ln x\) for all \(x\in {{\mathbb{R}}_{++}}\)