Excalibur0126
contestada

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

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

Respuesta :

meerkat18
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.

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