I have no idea what the question is asking by "a pattern". Does it mean the limitations of the inverse?Find a pattern for $\displaystyle f^{-1}(x)$ if

$\displaystyle f(x) = \frac {a^x +1}{a^x -1}$

where $\displaystyle a>0, a \neq 1$.

I also tried to solve it by switching the "x" values with "y" values and working from there but I got stuck at $\displaystyle x(a^y - 1) = a^y +1$.