Question 343867
Interchange {{{x}}} and {{{y}}} in the original equation.
{{{highlight(x)=4(2*highlight(y)-3)^(1/3)}}}
and solve for {{{y}}}. 
The new {{{y}}} is the inverse.
{{{x^3=64(2y-3)}}}
{{{x^3/64=2y-3}}}
{{{2y=x^3/64+3}}}
{{{highlight_green(yinv=(1/128)*x^3+3/2)}}}