Let \(f:W \to W\) be defined as $f(n)=n$ - $1$, if \(n\;is\;odd\;and\; f(n)=n+1,\;if\;n\;is\; even.\) Show that \(f\) is invertible. Find the inverse of \(f\). Here, \(W\) is the set of all whole numbers.

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