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

(A) There exists an onto function f: N → N such that fog = f

(B) There exists a one-one function f: N → N such that fog = f

(D) There exists a function: f: N → N such that gof = f

Sets, Relations and Functions: JEE Main 2021 Mathematics question

JEE Main 2021 · 25 Jul, Morning shift · Q3804

JEE Main 202125 Jul, Morning shiftMathematicsMediumSets, Relations and Functions168× since 2002

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?

JEE Main 2021 · 25 Jul, Morning shift · Q3804

JEE Main 202125 Jul, Morning shiftMathematicsMediumSets, Relations and Functions168× since 2002

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?