Question 930521
find the inverse of {{{f(x)=x^3+8}}}:

first, recall that {{{f(x)=y}}}

{{{y=x^3+8}}} ...now, swap {{{x}}} and {{{y}}}

{{{x=y^3+8}}} ...solve for {{{y}}}

{{{x-8=y^3}}}

{{{root(3,(x-8))=y}}}

so, inverse is

{{{f^-1(x)=root(3,(x-8))}}} or  {{{f^-1(x)=(x-8)^(1/3)}}}