Inverse Function of $ f(x) = \frac{1-x^3}{x^3} $ I need to show that these function has a continuous inverse function and find this inverse function.
$$ f(x) = \frac{1-x^3}{x^3} $$
Defined on $ (1,\infty) $
I think I need to check for bijectivity. Don't know how.
I tried to solve the function to $x$ then. But somehow I only end up with $ -\frac{1}{x^3} = -1 -y $ and don't know how to get to $x = ...$
Maybe there is no inverse function!? Or maybe just on the defined area? I don't know.

Let $$y=\frac{1-x^3}{x^3}$$ then $$y=\frac{1}{x^3}-1$$
then we have $$x=\frac{1}{\sqrt[3]{1+y}}$$
