1. Given two functions f and g, prove that f = g iff dom f = dom g and for every x ∈ dom f, f (x) = g(x). 2. Suppose that f : A → B, g: B → C, and h: C → D. Prove that h ° ( g ° f ) = (h ° g) ° f . 3....

1. Given two functions f and g, prove that f = g iff dom f = dom g and for every x ∈ dom f, f (x) = g(x).

2. Suppose that f : A → B, g: B → C, and h: C → D. Prove that h ° ( g ° f ) = (h ° g) ° f .

3. Let f : A → B and g : B → C. Using the ordered pair definition of the composition g ° f , prove that g ° f is a function and that g ° f : A → C.

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