Let $f : S^1 \rightarrow \mathbb{R}$ be a continuous map. Show that there exists a point x in $S^1$ s.t. $f(x) = f(-x)$.
Thank you.
2026-04-11 14:31:13.1775917873
Continuous function between real line and unit circle
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Hint: $f(x)=f(-x) \iff f(x)-f(-x)=0$