jmc

We are asked to find the largest value of $x=f^{-1}(y)$, that is the largest value of $x$ for which $f(x)$ exists. Since the point farthest to the right on the graph of $f$ is (6,0), this value is $x=\boxed{6}$. To say it another way, the maximum value of $f^{-1}(x)$ is the largest number in the domain of $f$.