as you may already know, to get the inverse of any expression, we start off by doing a quick switcharoo on the variables, and then solve for "y".
[tex]\bf \stackrel{f(x)}{y}=\sqrt[3]{x-4}\qquad \stackrel{inverse}{\underline{x}=\sqrt[3]{\underline{y}-4}}\implies x^3=y-4\implies x^3+4=\stackrel{f^{-1}(x)}{y}[/tex]
