Question 717175
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Replace *[tex \LARGE f(x)] with *[tex \LARGE y]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ 2x\ -\ \frac{1}{3}]


Solve for *[tex \LARGE x] in terms of *[tex \LARGE y]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{1}{2}y\ +\ \frac{1}{6}]


Verification of the steps required is left as an exercise for the student.


Swap the variables:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{1}{2}x\ +\ \frac{1}{6}]


Replace *[tex \LARGE y] with *[tex \LARGE f^{-1}(x)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f^{-1}(x)\ =\ \frac{1}{2}x\ +\ \frac{1}{6}]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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