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.

The original function $f$ takes an $x$ and spits out $y=f(x)$. The inverse is a function $g$ that takes any $y$ from the range of $f$ and spits out $x=g(y)$ such that $g(f(x))=x$ for any $x$ in the domain. So you want to solve for $y$ - you already almost got the correct answer. Once you get $x=g(y)$ for some function $g$, check that $g(f(x)) = x$ to make sure.
