The map

F : R³ \ (0,0,0) → R³ \ (0,0,0):v→(v/((v⋅v)))

is called inversion with respect to S². Let S be a surface that does not pass

through the origin, and let S' = F(S). Show that, if S is orientable, then so is

S' . Do this by showing that if N is the unit normal of S at a point p, then the

unit normal N' of S' at F(p) is

N'=[((2p⋅N)p/(|p|²)]-N

I have tried using a general parametrisation in terms of u and v, and three arbitrary functions f, g, and h for each component.I have then constructed the normal by the cross product of the partial derivatives.Now since S is an orientable surface this implies that this cross product is never zero. Then to obtain the unit normal i divide by the magnitude. At this point i am completely stuck