Discuss the below:
Q: Let f: A →B and g: B →C be functions.
a) Suppose that f and g are injective. Show that g o f is injective.
b) Suppose that f and g are surjective. Show that g o f is surjective.
c) Suppose that f and g are bijective. Then g o f is bijective by parts a) and b). Show that (gof)^-1 = f^-1 o g^-1.