(a) Let g: Rm R be a convex function, A an m n matrix, and b a vector in Rm. Show that is a convex function. (b) f(x) = g(Ax+b) Let h R R be a convex function, and let a ER, ER be scalars with a 0. Show that f(x) = ah(x) + B is a convex function. Hint: Make use of composition (see Exercise 3.2).