The given function is
[tex]h(x)=x^3-4[/tex]We have to find
[tex]h^{-1}(x)^{}[/tex]This means we have to find the inverse of h(x).
First, we isolate x.
[tex]\begin{gathered} y=x^3-4 \\ y+4=x^3 \\ x=\sqrt[3]{y+4} \end{gathered}[/tex]Then, we change the position of the variables.
[tex]y=\sqrt[3]{x+4}[/tex]