2.9.3

(g of) : A C. Explain carefully why this, together with a result proved in the text of this section, implies that the composition of two bijections is a bijection. P2.9.3 Let f : A-+ B and g : B-+ C be functions such that go f s a bijection. Prove that f must be one-to-one and that g must be onto. Give an example showing that it is possible for neither fnor g to be a bijection