Let $f: \mathbb{R}^n \rightarrow \mathbb{R}_{\geq 0}$ be continuous.
Consider $g: \mathbb{R}_{\geq 0} \rightarrow \mathbb{R}_{\geq 0}$ strictly increasing, continuous and such that $g(0)=0$.
I think this is an interesting (maybe trivial) question:
are $f(\cdot)$ and $g(f(\cdot))$ sharing the same minima?