I have the following question, but don't know how to start for finding order of a function defined on a symetric group.
Question:
Consider the symetric group $S_X$ on the set $ X = \mathbb{R} - \{0, 1\}$. Let $f$ be the function defined by the following rule
$f(x) = (x-1)/x$
for all $x \in X$. Show that $f \in S_X$, and find the order of $f$ and the inverse of $f$.
I feel like the order of $f$ should be infinity but I am not sure.