Question

Please help! I have very limited time to answer, but I am really stumped!

Answer 1

Answer:

A

Step-by-step explanation:

So we have the function:

$f(x)=y=\sqrt[3]{x-2}+8$

To find the inverse of the function, we can flip x and y and then solve for y. Therefore:

$x=\sqrt[3]{y-2}+8$

Solve for y to find our inverse.

Subtract 8 from both sides:

$x-8=\sqrt[3]{y-2}$

Cube each side. The right cancels:

$(x-8)^3=y-2$

Add 2 to both sides:

$y=(x-8)^3+2$

Therefore, our inverse is:

$f^{-1}(x)=(x-8)^3+2$

The answer is A