Answer
$f^{-1}(x) = (x+2)^{\frac{1}{3}}$
Work Step by Step
$f(x) = x^{3} -2$
Let $f(x) = y$
$y = x^{3} - 2$
$x = y^{3} - 2$
$x + 2 = y^{3}$
$(x+2)^{\frac{1}{3}} = y$
$f^{-1}(x) = (x+2)^{\frac{1}{3}}$
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