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Let $f, g:[0,1] \to [0, \infty]$ be continuous. Assume $f(x)>g(x)$ for all $x \in [0,1]$. Prove that there exists a $M>1$ such that $f(x) \ge M g(x)$ for all $x \in [0,1]$.

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merged by Eric Naslund Dec 21 '12 at 0:26

this question was merged with Prove existence of $c$ such that $f(x)\ge c g(x)$ because it is an exact duplicate of that question.