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]\bf \stackrel{g(x)}{y}=-1+(x-1)^5\implies \stackrel{\textit{switcheroo}}{\underline{x}=-1+(\underline{y}-1)^5}\implies x+1=(y-1)^5 \\\\\\ \sqrt[5]{x+1}=y-1\implies \sqrt[5]{x+1}+1=\stackrel{g^{-1}(x)}{y}[/tex]
