Answer
$f^{-1}(-6)=-2$
Work Step by Step
To find $f^{-1}(-6)$ means that you have to look for the value of $x$ such that $f(x) = -6$.
To achieve this, substitute -6 to $f(x)$ to have:
$f(x) = x^3+2
\\-6 = x^3 + 2
\\-6-2 = x^3
\\-8=x^3
\\\sqrt[3]{-8} = x
\\-2=x$
Therefore $f^{-1}(-6) = -2$.
