Question: Determine whether

1. Reciprocals of positive concave functions are convex
2. Reciprocals of positive convex functions are concave
3. There exists a convex function \(f:{{\mathbb{R}}_{++}}\to \mathbb{R}\) such that \(f\left( x \right)\le \ln x\) for all \(x\in {{\mathbb{R}}_{++}}\)

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