Let f:X-->R^n. Then, f is affine if X is a convex set and f(ax + (1-a)y) = af(x) + (1-a)f(y) for all x, y in X and a in [0, 1]. Equivalently, f is affine if it is both convex and concave. Moreover, if X=R^n, f is the translation of a linear function: ax+b.

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