[tex]\begin{gathered} f(x)=5(x+3)^3-2 \\ \text{let f(x) = y} \\ y=5(x+3)^3-2 \\ x=5(y+3)^3-2 \\ or \\ 5(y+3)^3-2=x \\ 5(y+3)^3=x+2 \\ (y+3)^3=\frac{x+2}{5} \\ y+3=\sqrt[3]{\frac{x+2}{5}} \\ y=\sqrt[3]{\frac{x+2}{5}}-3 \\ f^{-1}(x)=\sqrt[3]{\frac{x+2}{5}}-3 \end{gathered}[/tex]
