Find f^(-1) for the function f(x)= \sqrt[3]{x-2}+8. A. f^(-1)(x)=(x-8)^3+2 B. f^(-1)(x)=(x+8)^3+2 C. f^(-1)(x)= \sqrt[3]{x-8} +2 D. f^(-1)(x)=(x-8)^3-2

Question

Find
`f^(-1)` for the function
`f(x)= \sqrt[3]{x-2}+8`.

A.
`f^(-1)(x)=(x-8)^3+2`
B.
`f^(-1)(x)=(x+8)^3+2`
C.
`f^(-1)(x)= \sqrt[3]{x-8} +2`
D.
`f^(-1)(x)=(x-8)^3-2`

Answer 1

The f⁻¹ means that you have to find the inverse of the given original function. The solution is shown below. First, interchange the x and y variables, then solve for y.

f(x) = ∛(x - 2) + 8
y = ∛(x - 2) + 8
x = ∛(y - 2) + 8
x - 8 = ∛(y - 2)
[x - 8 = ∛(y - 2)]³
(x - 8)³ = y - 2
y = (x - 8)³ + 2
f⁻¹(x) = (x - 8)³ + 2

The answer is A.