f(x) = g(x) for all xe [-1,-e]U[e, 1], and g(x) f(x) for all x = [-1,1]. Exercise 3.2.19 (Challenging): A function f: I→ R is convex if whenever a <x<b for a,x,b in 1, we have f(x)f(a)(b). In other words, if the line drawn between (a, f(a)) and (b, f(b)) is above the graph of f a) Prove that if I= (a,ß) an open interval and f: I-R is convex, then f is continuous. b) Find an example of a convex f: [0,1]R which is not continuous.