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