Stuck on solving an analysis problem

timer Asked: Dec 17th, 2014

Question description

Suppose that f is continuous on [0,2] and that f(0)=f(2).  Prove that there exist x,y in [0,2] such that absolutevalue(y-x)=1 and f(x)=f(y).  Hint: consider g(x)=f(x+1)-f(x) on [0,1].

here is what I have:

let g(x)=f(x+1)-f(x) be continuous on [0,1]


g(1)=f(2)-f(1) since f(2)=f(0)   g(1)=f(0)-f(1)=-(f(1)-f(0))

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