For the problem f(x) = 1 - ln(x - 2) how would I find the inverse (f^-1) ? And how would I confirm that algebraically?

Thanks.

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- Jul 5th 2010, 07:17 PMstrawberryPKinverse function of natural log?
For the problem f(x) = 1 - ln(x - 2) how would I find the inverse (f^-1) ? And how would I confirm that algebraically?

Thanks. - Jul 5th 2010, 07:20 PMProve It
You have $\displaystyle y = 1 - \ln{(x - 2)}$.

To find the inverse function, swap your $\displaystyle x$ and $\displaystyle y$ values...

$\displaystyle x = 1 - \ln{(y - 2)}$

$\displaystyle \ln{(y - 2)} = 1 - x$

$\displaystyle y - 2 = e^{1 - x}$

$\displaystyle y = 2 + e^{1 - x}$.

So $\displaystyle f^{-1}(x) = 2 + e^{1 - x}$.