Inverse of a particular function

Question

How can we compute the inverse of the function

$$f(n)=\frac{a^{n(n+1)}}{b^n}$$

where $a$ and $b$ are positive constants?

Answer 1

Hint:

Taking log base $e$ on both sides to get:

$n^2\ln a+n\ln(\frac{a}{b})-\ln y=0$

This is quadratic in $n$ and you will obtain $n$ as a function of $y$. Hopefully that helps.