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Limits & Continuityhard
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Let f:[0,1]→Rf: [0, 1] \to \mathbb{R}f:[0,1]→R be a continuous function such that f(0)=f(1)f(0) = f(1)f(0)=f(1). Define g(x)=f(x+1n)g(x) = f(x + \frac{1}{n})g(x)=f(x+n1​) for a fixed integer n>1n > 1n>1. Which of the following statements must be true?