Let f: A->B be a bijection, where A and B are subsets of the set of all real numbers. Prove that if f is increasing on A, then f's inverse is increasing on B.
My professor said to use the contrapositive of "f: A->B is increasing" to prove this, but I don't understand how that would help me.
I know that if f is a bijection and g is the inverse of f, then g is also a bijection and f is the inverse of g.
I don't even know where to start.