Answer
The inverse function is $~~f^{-1}(x) = -ln(x-1)$
We can see that the graphs are reflections about the line $y=x$
Work Step by Step
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 $y=x$
