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Given two convex functions ( f(x) and g(x) ) and two parameters α and β satisfying...

Given two convex functions ( f(x) and g(x) ) and two parameters α and β satisfying α+β=1.

(a) The function αf(x)+βg(x) is convex

(b) The function αf(x)-βg(x) is convex

(c) The function αf(x)-βg(x) is convex when g(x) is linear

(d) None of the above statements is correct

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