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Nov 8, 2009 at 15:07 comment added fedja The problem is exclusively how to figure out the domain. The "formula" for the inverse is as easy as the integer closest to the rough approximation you can get from the asymptotics. It is the same as with $x^5+5x$: if you want to invert it on positive integers, the formula for the inverse function is merely $y\mapsto [\sqrt[5]y]$ for all sufficiently large $y$.
Nov 8, 2009 at 6:05 history answered engelbrekt CC BY-SA 2.5