Answer & Explanation
As Arturo Magidin said in the comments, it is a matter of notation. Usually, denote respectively, when n=1,2,…. Unfortunately, due to various historical reasons, when n=−1, the notation do not at all mean 1 divided by the respective functions, but rather represent the inverse function.
Your confusion probably comes from your teacher/textbook using to mean instead of or . This confusing notation unfortunately rather common. The good news is that there's nothing conceptual you're missing, it's just an instance of particularly confusing notation.