JEE Math Practice Question

Let g : N $$\to$$ N be defined as g(3n + 1) = 3n + 2, g(3n + 2) = 3n + 3, g(3n + 3) = 3n + 1, for all n $$\ge$$ 0. Then which of the following statements is true?

1. A.There exists an onto function f : N $$\to$$ N such that fog = f
2. B.There exists a one-one function f : N $$\to$$ N such that fog = f
3. C.gogog = g
4. D.There exists a function : f : N $$\to$$ N such that gof = f