Let f : A B and g : B C be functions. Prove it if is true and give a counterexample if is false

A) Prove that If g f is one-to-one (injective), g must also be one-to-one (injective).

B) Prove that If g f is onto (surjective), g must also be onto (subjective).

C) Prove that If f has a well-defined inverse(bijective), g f must also have a well-defined inverse(bijective).