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Let g : N \(\to\) N be defined as ,\(\text{g}\left(3\text{n}+1\right)=3\text{n}+2\), \(\text{g}\left(3\text{n}+2\right)=…

Q1

Let g : N \(\to\) N be defined as ,\(\text{g}\left(3\text{n}+1\right)=3\text{n}+2\), \(\text{g}\left(3\text{n}+2\right)=3\text{n}+3\), \(\text{g}\left(3\text{n}+3\right)=3\text{n}+1\) for all \(\text{n}\geq 0\)

Then which of the following statements is true ?

[JEE Main 2021, 25 Jul (Shift 1)]

a

There exists a function \(\text{f}:\text{N}\to \text{N}\) such that \(gof=f\)

b

\(\text{gogog}=\text{g}\)

c

There exists a one-one function \(\text{f}:\text{N}\to \text{N}\) such that \(fog=f\)

d

There exists an onto function \(\text{f   }:N\to N\) such that \(fog=f\)

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