Question 146994
To find the inverse of a function, first use x and y as dependent and independent variables. 
{{{f(x)=(x-1)^(1/3)}}}
{{{y=(x-1)^(1/3)}}}
Now interchange x and y and solve for y.
{{{y=(x-1)^(1/3)}}}
{{{highlight(x)=(highlight(y)-1)^(1/3)}}}
{{{y-1=x^3}}}
{{{y=x^3+1}}}
{{{f^(-1)(x)=x^3+1}}}