TITLE: A question about primitive recursive functions
QUESTION [5 upvotes]: I have a question about primitive recursive functions. Maybe it's trivial, if it is I will move it into math.stackexchange.
Is there a primitive recursive function $f$ which is a bijection of $N$ onto $N$ such that $f^{-1}$ is not primitive recursive ?

REPLY [3 votes]: More concisely, it is not far from the truth to say that the purpose of (adding) the minimalisation operation for general recursion is to define inverse functions. That this is Difficult is put to practical use in many methods of encryption.