A function is C diffeomorphic if it is a C function, it's inverse is a C function and they are both bijective. Consider the maps F : Bn Rn and G : Rn Bn, F ( x) = x 1 | x|2 , and G( y) = y 1 + | y|2 , where the manifold Bn is the open unit ball in Rn. These maps are both diffeomorphic. Prove that they are inverses of each other, which helps to prove that the open unit ball is diffeomorphic to Rn