Question 520152
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Solve for *[tex \Large x] in terms of *[tex \Large y] and then swap the variables.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ (x\ +\ 4)^3]


Take the cube root:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt[\small{3}\LARGE]{y}\ =\ x\ +\ 4]


Add -4 to both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt[\small{3}\LARGE]{y}\ -\ 4\ =\ x]


Swap the variables:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \sqrt[\small{3}\LARGE]{x}\ -\ 4]


Then substitute inverse function notation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f^{-1}(x)\ =\ \sqrt[\small{3}\LARGE]{x}\ -\ 4]


Write back and I'll send you a graph of both functions.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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