Answer:
A
Step-by-step explanation:
So we have the function:
[tex]f(x)=y=\sqrt[3]{x-2}+8[/tex]
To find the inverse of the function, we can flip x and y and then solve for y. Therefore:
[tex]x=\sqrt[3]{y-2}+8[/tex]
Solve for y to find our inverse.
Subtract 8 from both sides:
[tex]x-8=\sqrt[3]{y-2}[/tex]
Cube each side. The right cancels:
[tex](x-8)^3=y-2[/tex]
Add 2 to both sides:
[tex]y=(x-8)^3+2[/tex]
Therefore, our inverse is:
[tex]f^{-1}(x)=(x-8)^3+2[/tex]
The answer is A
