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October 10th, 2012, 10:49 PM   #1
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Concave Function of a Convex Function

F(x) and f(x) are respectively a concave and a convex function in x. Is it possible to say anything regarding the nature (concavity and convexity) of the composite function F(f(x))? If there exists a definite result, an outline of the proof will be appreciated.
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