1. Find an example of functions f : A → B and g : B → C such that g and g ° f are both surjective, but f is not surjective. 2. Find an example of functions f : A → B and g : B → C such that g ° f is...

1. Find an example of functions f : A → B and g : B → C such that g and g ° f are both surjective, but f is not surjective.

2. Find an example of functions f : A → B and g : B → C such that g ° f is bijective, but neither f nor g is bijective

3. Let f : A → B and suppose that there exists a function g : B → A such that g ° f = iA and f ° g = i_B.

(a) Prove that f is bijective.

(b) Prove that g = f^–1.