Is it true that for a function $f(x): \mathbb{R} \to [0,\infty)$ it holds$$\sup[f(x)^a] \leq [\sup(f(x))]^a $$for $a \in (-\infty,+\infty)$?
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Is it true that for a function $f(x): \mathbb{R} \to [0,\infty)$ it holds$$\sup[f(x)^a] \leq [\sup(f(x))]^a $$for $a \in (-\infty,+\infty)$?