Question

Find latex-formula"> 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.