Let $f(x)$ be a continuous function defined from $f(x):R\to{A}$, where $A$ is a bounded closed interval. If I can prove that end points of $A$ are global maxima and global minima of $f(x)$, Is $f(x)$ always onto(surjective) or there are some exceptions?
2026-03-25 01:22:23.1774401743
Proving $f(x)$ is onto using maxima/minima
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No, there are no exceptions, by the intermediate value theorem.