SOLUTION: Given the one-to-one function f(x) =(x-2)^3,find the inverse function

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Question 959110: Given the one-to-one function f(x) =(x-2)^3,find the inverse function
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Basic steps:
1) Replace f(x) with y
2) Swap x and y
3) Solve for y

f%28x%29=%28x-2%29%5E3

y=%28x-2%29%5E3

x=%28y-2%29%5E3

root%283%2Cx%29=y-2

root%283%2Cx%29%2B2=y

y=root%283%2Cx%29%2B2

y=2%2Broot%283%2Cx%29

The inverse function is f^{-1}(x) = 2+\sqrt[3]{x}
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