inverse function of natural log?

**strawberryPK** · July 5th 2010, 07:17 PM

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.

**Prove It** · July 5th 2010, 07:20 PM

You have $y = 1 - \ln{(x - 2)}$ .

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

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

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

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

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

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

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