Question 320812
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Replace *[tex \LARGE f(x)] with *[tex \LARGE y].


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ 5^{x\,+\,6}\ -\ 7]


Solve for the independent variable in terms of the dependent variable.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ +\ 7\ =\ 5^{x\,+\,6}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ln(y\ +\ 7)\ =\ \ln\left(5^{x\,+\,6}\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ln(y\ +\ 7)\ =\ (x\ +\ 6)\ln\left(5\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\ln(y\ +\ 7)}{\ln\left(5\right)} =\ x\ +\ 6]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ = \frac{\ln(y\ +\ 7)}{\ln\left(5\right)}\ -\ 6]


Swap positions of the variables and set the resulting expression equal to *[tex \LARGE f^{-1}(x)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f^{-1}(x)\ = \frac{\ln(x\ +\ 7)}{\ln\left(5\right)}\ -\ 6]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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