Question: Let f : [0, 2?] > R be a continuous function such that f(0) : f(27r). Prove that there is an ;T.'- E [0, 7r]

Let f : [0, 2?] > R be a continuous function such that f(0) : f(27r). Prove that there is an ;T.'- E [0, 7r] such that f(:r) : f (:1: + 3T). Another way to state this problem is to consider a continuous function from a circle to the real numbers. Then, there are two Opposite points which have the same value. (the only thing you need to know from 7? for this problem is that \"It 2 0)

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