Is there a mathematical function which flips 1 and 2?

Question

I'm looking for a function $f : \mathbb{Z} \rightarrow \mathbb{Z}$ such that $f(f(x)) = x$ and $f(1) = 2$. In particular, I don't want this function to be a piecewise function. Does such a function even exist?

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For example, I can define the above function as follows:

\begin{equation} f(x) = \begin{cases} 2 & x = 1 \\ 1 & x = 2 \end{cases} \end{equation}

However, I was wondering whether there's a way to define this function without writing conditions.

Answer 1

$3-x$ (plus enough characters to qualify as an answer).

Answer 2

How about $f(x) = x-(-1)^x$? That works.