we are given
[tex] f(x)=\sqrt[3]{x+2} [/tex]
Firstly , we set f(x)=y
[tex] y=\sqrt[3]{x+2} [/tex]
now, we can switch x and y
[tex] x=\sqrt[3]{y+2} [/tex]
now, we can solve for y
[tex] x^3=(\sqrt[3]{y+2})^3 [/tex]
[tex] x^3=y+2 [/tex]
[tex] y=x^3-2 [/tex]
so, our inverse function is
[tex] f^{-1}(x)=x^3-2 [/tex]............Answer
[tex]f(x)=\sqrt[3]{x+2}\to y=\sqrt[3]{x+2}[/tex]
we replace x with y
[tex]\sqrt[3]{y+2}=x\ \ \ \ |^3\\\\y+2=x^3\ \ \ \ |-2\\\\y=x^3-2[/tex]
Answer: [tex]f^{-1}(x)=x^3-2[/tex]
