Let g : N $\to$ N be defined asg(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?

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?

There exists an onto function f : N $\to$ N such that fog = f

There exists a one-one function f : N $\to$ N such that fog = f

gogog = g

There exists a function : f : N $\to$ N such that gof = f

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