Answer
$f^{-1}(x)=(x-1)^3$
Work Step by Step
$f(x)=x^{\frac{1}{3}}+1,$
$y=x^{\frac{1}{3}}+1,$
$x=y^{\frac{1}{3}}+1,$
$x-1=y^{\frac{1}{3}},$
$(x-1)^3=y=f^{-1}(x),$
Checking the Inverse function..
$(f^{-1}\circ f)(x)=(x^{\frac{1}{3}}+1-1)^3=(x^{\frac{1}{3}})^3=x,$
$(f\circ f^{-1})(x)=[(x-1)^3]^{1/3}+1=x-1+1=x$
