Why is the point $x=0$ not a periodic point of $f(x)=1/x$ of period $2$?

Question

In a question I am trying to solve, I am asked to prove that $x=0,1$ and $-1$ are not points of period $2$ for $f(x)=1/x$. I get why $x=1,-1$ aren't points of period $2$ but why is $x=0$ not a periodic point because

$$ f(f(x))=x $$

and so $f^{[2]}(0)=0$. Why is this wrong?

Answer 1

What is $f(0)$? The way you have defined $f(x)$, $0$ is not in the domain, so it doesn't make sense to talk about periodicity of the point.