Answer:
we will assume Ker f = {0} or Ker f = F
when Ker f = 0 ( nothing to prove )
but when Ker f = F
f ( x ) = 0 , ∀x ∈ F
as ⇒Im F = 0
but when F = R and R ≠ 0 , it proves that ker f = {0}
and this proves that f is an isomorphism
Step-by-step explanation:
F been a subjective homomorphism shows that f is one-one
Therefore to prove that f is an isomorphism
we will assume Ker f = {0} or Ker f = F
when Ker f = 0 ( nothing to prove )
but when Ker f = F
f ( x ) = 0 , ∀x ∈ F
as ⇒Im F = 0
but when F = R and R ≠ 0 , it proves that ker f = {0}
and this proves that f is an isomorphism
