hallow guyz its my firts time to have such interaction over this forum !!

I've encouter lil diffeculty to go thru this proof , any body can assist me ??


let B^n ∁ R^n denote the open unit ball in R^n with center at the orgine.i.e
B^(n )={x∈R^n:|x|<1}then how I can show or Prove the map f:R^n-→B^ given by
f:x⟼x/(1+|x| ) ϵB^n
is well defined and gives a homeomorphism B^n ≅ R^n . thanx in advance !