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