## Calculus: Early Transcendentals 8th Edition

The inverse function is $~~f^{-1}(x) = -ln(x-1)$ We can see that the graphs are reflections about the line $y=x$
We can solve $f$ for $x$: $y = 1+e^{-x}$ $y-1 = e^{-x}$ $ln(y-1) = -x$ $x = -ln(y-1)$ We reverse the places of $x$ and $y$: $y = -ln(x-1)$ The inverse function is $~~f^{-1}(x) = -ln(x-1)$ When we graph the two functions $f(x)$ and $f^{-1}(x)$ along with the line $y=x$, we can see that the graphs are reflections about the line $y=x$