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Let f((x+y)/(2))=(1)/(2)[f(x)+f(y)] for ...

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

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The correct Answer is:
`(-1)`
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