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Let f((x+y)/2)=(f(x)+f(y))/2 for all rea...

Let `f((x+y)/2)=(f(x)+f(y))/2` for all real x and y. If f'(0) exists and equals -1 and f(0)=1, find f(2)

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The correct Answer is:
`f'(x) = -1`
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