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🛠️ JEE➗ Maths

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

Q1

Let \(g:N\to N\) be defined as

\(\begin{matrix}g(3n+1)=3n+2, \\ g(3n+2)=3n+3,\end{matrix}\\ g\left(3n+3\right)=3n+1,\text{ for all }n\geq 0\)

Then which of the following statements is true?

JEE MAINS[2021]

a

There exists a function \(f: N \rightarrow N\) such that \(g \circ f =f\)

b

\(g \circ g \circ g=g\)

c

There exists a one-one function \(f: N \rightarrow N\) such that \(f \circ g =f\)

d

There exists an onto function \(f: N \rightarrow N\) such that \(f \circ g=f\)

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