Please solve all parts

Problem 1. (10 points) a. Give explicit formulas for functions from the set Z of integers to the set N that are: i. One-to-one but not onto ii. iii. iv. Onto but not one-to-one One-to-one and onto Neither one-to-one nor onto If functions f and f g are both onto, does it follow that g is onto? Prove or give a counterexample. Let A, B, and C be sets, and let f: B C and g: A B be functions. Let h: A C be the composition, f o g, that is, h(x) = f(g(x)) for x counterexample, for each of the following claims: b. C. E A. Prove, or give a i. If h is surjective, then f must be surjective. ii. If h is surjective, then g must be surjective. ii. If h is injective, then f must be injective. iv. If h is injective and f is total1, then g must be injective