JEE Main 2021 (25 Jul, Shift 1) Maths Q66: Let be defined…

Question

Let $g:\mathbf{N}	o\mathbf{N}$ be defined as
$g(3n+1)=3n+2$,
$g(3n+2)=3n+3$,
$g(3n+3)=3n+1$, for all $n\ge0$.
Then which of the following statements is true ?

Accepted Answer

Option 3: There exists an onto function $f:\mathbf{N}	o\mathbf{N}$ such that $fog=f$

Answer

$gogog=g$

Answer

There exists a one-one function $f:\mathbf{N}	o\mathbf{N}$ such that $fog=f$

Answer

There exists an onto function $f:\mathbf{N}	o\mathbf{N}$ such that $fog=f$

Answer

There exists a function $f:\mathbf{N}	o\mathbf{N}$ such that $gof=f$

JEE Main 25 July 2021, Shift 1, Maths Q66