Answer the following questions about convexity: Find all convex and twice differentiable functions f(x) : R -> R for which e^f(x) is convex. Prove or disprove the following statement: Given an arbitrary function h(x) : R^n -> R, the function h(x) must be convex if the set {x in R^n | h(x) <= 0} is convex. Given an arbitrary convex function h(x) : R^n -> R, prove that {x in R^n | h(x) <= 0} is a convex set. Prove or disprove that the set {x in R^2 | e^{x1+x2} + (x1 - x2)^2 <= 1, x1^2 + x1x2 + x2^2 <= 5} is convex.