f, g : N -> N (Natural Numbers including zero)

f is injective but not surjective

g is surjective but not injective

1) Is it possible for (f composit g) to be a bijection?

2) Is it possible for (g composit f) to be a bijection?

3) Would the answers 1) and 2) be different if the natural numbers did not include zero?

Thank you for your help!