Answer:
[tex]f^{-1}(x)=\sqrt[3]{x-7}[/tex]
Step-by-step explanation:
First let me list the steps to find the inverse of a function.
1) Replace f(x) with y
2) Swap the locations of x's and y's
3) Solve for y
4) Replace y with [tex]f^{-1}(x)[/tex]
Now lets do this with this function
[tex]f(x)=x^3+7\\\\y=x^3+7\\\\x=y^3+7\\\\y^3=x-7\\\\y=\sqrt[3]{x-7}\\\\f^{-1}(x)=\sqrt[3]{x-7}[/tex]
