as you already know, to find the inverse expression we start off by doing a quick switcheroo on the variables, and then we solve for "y".
[tex]\bf \stackrel{h(x)}{y}=\sqrt[5]{6x-12}+1\implies \stackrel{switcheroo}{x=\sqrt[5]{6y-12}+1}\implies x-1=\sqrt[5]{6y-12} \\\\\\ (x-1)^5=6y-12\implies (x-1)^5+12=6y\implies \cfrac{(x-1)^5+12}{6}~~=~~\stackrel{f^{-1}(x)}{y}[/tex]
