I need to find the domain and range of the inverse of this function:

$\displaystyle f(x)=x^3+2$

I ended up with $\displaystyle f^{-1}(x)=\sqrt[3]{x-2}$ as the inverse . . I think . . . All the examples I have come across with inverses do not have a cube root, only square root.

(Crying) So confused.