Suppose : R ⟶ R is increasing and convex on its domain , . Let denote its inverse, i.e., the function with domain ( ), ( ) and = for < < . What can you say about the convexity or concavity of ?

Suppose f: R ⟶ R is increasing and convex on its domain (a,b) . Let g denote its inverse, i.e., the function with domain (f(a),  f(b)) and g(f(x))= x for a