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Let f:R-->R be continuous and satisfy |f(x)-f(y)|>or eq. to k|x-y| for all x, y in R and some k>0. Show that f is surjective.

I can show that f is injective: let f(x) = f(y), hence k|x-y|< or eq. to 0, thus x=y.

I had a suggestion that it might be helpful to show that f has closed image. But I don't see how to work with that.

I know that f is surjective if for each y in R there is an x in R such that f(x)=y.

I don't see how to proceed.

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# Homework Help: Surjective function

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