Answer
f and g are inverses of each other
Work Step by Step
g(f(x)) = $g(x^{3} + 1) = (x^{3} + 1 - 1)^{\frac{1}{3}}$ = x
f(g(x)) = $f((x - 1)^{\frac{1}{3}})$ = ${(x - 1)^{\frac{1}{3}}}^{3} + 1$ = x - 1 + 1 = x
Since g(f(x)) = f(g(x)), f and g are inverses of each other
