Let f : A → and g : B → C and define g o f : A → C by (g o f)(x) := g(f(x)).
a) Show that if f, g are 1-1 (respectively, onto), then g o f is 1-1 (respectively, onto).
b) Prove that if f is 1-1 from A into B and B0: = {y : y = f(x) for some x ∈ A}, then f-l is 1-1 from B0 onto A.
c) Suppose that g is 1-1 from B onto C. Prove that f is 1-1 on A (respectively, onto B) if and only if g o f is 1-1 on A (respectively, onto C).