as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solve for "y".
[tex]\stackrel{f(x)}{y}=\sqrt[3]{x^5-3}\implies \stackrel{\textit{quik switcheroo}}{x = \sqrt[3]{y^5-3}}\implies \stackrel{\textit{cubing both sides}}{x^3=y^5-3} \\\\\\ x^3+3=y^5\implies \sqrt[5]{x^3+3}=\stackrel{f^{-1}(x)}{y}[/tex]
