If the function $f:\mathbb{N}\to\mathbb{N}$ is defined as $$f(x)=\begin{cases}{n-1} & {,\, If\, \, n\, \, is\, \, even} \\ {n+1} & {,If\, n\, is\, odd}\end{cases}$$ then
(A) $f$ is injective
(B) $f$ is into
(C) $f$ is surjective
(D) $f$ is invertible
Choose the correct answer from the options given below :