One way to find the inverse of an equation is to reverse the variables $x$ and $y$ (this corresponds to reflection over the line $y=x$) and then solve the resulting equation for $y$. In this case, you don't need to actually find the inverse, just compute a specific value. If we have
then we can write the inverse as
Since this second equation is the inverse of the inverse, it is the original equation $f(x)$. We want to find the $x_0$ such that $f(x_0)=1$. By the identification of $y$ with the function, all we have to do to find $x_0$ is plug in $y=1$.
EDIT: Brian's answer is exactly what I've done, only written with better notation. Use that since it makes that relationships much clearer than hiding it behind another variable $y$.