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

Step-by-step solution

g : N → N g ( 3 n + 1 ) = 3 n + 2 g ( 3 n + 2 ) = 3 n + 3 g ( 3 n + 3 ) = 3 n + 1 g x = x + 1 ; x = 3 k + 1 x + 1 ; x = 3 k + 2 x - 2 ; x = 3 k + 3 g g x = x + 2 ; x = 3 k + 1 x - 1 ; x = 3 k + 2 x - 1 ; x = 3 k + 3 g g g x = x ; x = 3 k + 1 x ; x = 3 k + 2 x ; x = 3 k + 3 If f : N → N , f is a one-one function such that f ( g ( x ) ) = f ( x ) ⇒ g ( x ) = x , which is not the case If f : N → N ,   f is an onto function such that f ( g ( x ) ) = f ( x ) one possibility is f x = n ; x =