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Find a continuous function over reals that takes on every value exactly three times.

I was thinking such a function would have to have two critical points and must go from increasing to decreasing or decreasing to increasing. Something like $x^3$, but still there are some points there that aren't counted three times. How would I go about constructing such a function?

user19405892
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1 Answers1

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Ethan Bolker
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  • What about its equation? – user19405892 Feb 27 '16 at 19:11
  • You'll find a formula at http://math.stackexchange.com/questions/735842/function-f-mathbbr-to-mathbbr-that-takes-each-value-in-mathbbr-th (from the comment above). If I'd seen that comment I wouldn't have posted my duplicate answer. – Ethan Bolker Feb 27 '16 at 23:58