If $f(x_1)=f(x_2)=y$, then prove that $f$ can not be continuous everywhere [duplicate]
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Can a continuous function from the reals to the reals assume each value an even number of times?
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Let $ f:[a,b]→mathbb R$ be a function with the following property: For every $yin f([a,b])$ , you have exactly two $ x_1, x_2 $ ,such as $f(x_1)=f(x_2)=y$ . Prove that f can not be continuous everywhere .
continuity definition
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edited Dec 18 '18 at 23:23
Martund
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