JEE Advance 2025 Paper 1

Consider functions $f \colon \mathbb{N} \to \mathbb{Z}$   where $f(n) = (n+1)/2$   if $n$   is odd and $(4-n)/2$   if $n$   is even, and $g \colon \mathbb{Z} \to \mathbb{N}$   where $g(n) = 3+2n$   if $n \ge 0$   and $-2n$   if $n < 0$  . Which statements are TRUE?