For some strictly non-negative function $f\,\colon \mathbb{R} \to \mathbb{R}^+$, and a monotonically increasing function $g\,\colon \mathbb{R} \to \mathbb{R}^+$, is there a name (theorem or lemma name?) to the result $$ \arg\min_{x \in \mathbb{R}} f(x) = \arg\min_{x \in \mathbb{R}} g(f(x)). $$
It seems obvious enough, so I am sure it must go by a more formal name. (I can consider smaller subsets of $\mathbb{R}$).