For each of the following functions, determine whether it is injective, surjective, both, or neither. Justify your answer. (Be careful to make sure you understand exactly what the domain and codomain are for each of these functions.)

a. f: N→ R with the assignment rule f(x) = 4x^2.
b. H: P2 → R with the assignment rule Hp) = 4p'(1) - 3. (Clarification: Here p is a polynomial, and p' (x) is the derivative of p, which is also a polynomial. Then p'(1) is a number, which you get from plugging in x = 1 into the polynomial p'(x).)
c. q: R → R x R with the assignment rule q(x) = (2x - x^3).