(a) Suppose that f is an injection. Show that f-1 f (x) = x for all...

(a) Suppose that f is an injection. Show that f-1 ο f (x) = x for all x ∈ D(f) and that f ο f-1(y) = y for all y ∈ R( f ).
(b) If f is a bijection of A onto B, show that f-1 is a bijection of B onto A.