Please help with problem 5 and 6.

Problem 5. Suppose f : N - N is surjective (onto). Define g : N XN - N as g( x, y) = f (x)f(y). Prove that g is surjective (onto). Problem 6. Suppose f : Z -> Z is injective (1-to-1). Define g : Z -> (Z x Z) such that g(x) = (2f(x), If(x)1). Prove that g is injective (1-to-1)