Existence of a point satisfying a given condition – math.stackexchange.com

Existence of a point satisfying a given condition – math.stackexchange.com

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Let $\mathbf{T}=\{z\in \mathbb{C} : |z|=1\}$ and $f:[0,1]\to \mathbb{C}$ be continuous with $f(0)=0, f(1)=2$. Show that $\exists n\in [0,1]$ such that $f(n)$ is in $\mathbf{T}$. I approached ...

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