This is probably similar to a question I recently asked, but I can't quite make he connection.

Question:

$\displaystyle g(x) = \frac{3x}{5+x^2}$

Given that the domain ofgis $\displaystyle x \geqslant a$, find the least value ofasuch thatghas an inverse function.

Drawing a graph of the function, I notice that the first positive maximum is $\displaystyle \sqrt{5}$, which incidentally also happens to be the answer to the question. Why is this?

Thank you in advance.