i want to find the domain of the inverse

There's essential two ways to find the domain of the inverse.
1. Solve for the inverse [tex]f^{1}[/tex]. Then find the vertical asymptote(there's one in the inverse function). Find the domain of [tex]f^{1}[/tex]
2. Find the range of the original function f. Find the horizontal asymptote in f. Find the range of the f= domain of [tex]f^{1}[/tex]
I do not get the same inverse function as you did. Show how you got that answer.
[tex]y = \frac{6}{x3}[/tex]

Even if you get the inverse function to be this, how did you get the range to be y<6? There's a horizontal asymptote at y=0