Question: Suppose that U and g are two twice differentiable functions of x, both of them increasing and concave, with U 0, U 0,

Suppose that U and g are two twice differentiable functions of x, both of them increasing and concave, with U’ ≥ 0, U” ≤ 0, g’ ≥ 0, and g” ≤ 0. Prove that the composite function f(x) = g(U(x)) is also increasing and concave.

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