1. Explain briefly and colloquially (no math required) what is a proof by contradiction. Then use a proof by contradiction to prove log4 (7) is an irrational number.

2. Suppose f and g are both one-to-one functions, and let h be the composition f and g; that is, h = f g. Prove h is a one-to-one function.

3. Find f 0 (x) where f(x) = ln |x|. Note: in this context x is a real number except it is not zero.