1. If the graph of the function $f(x)$ is a broken line connecting the points $(0,0),(1,1)$, and $(2,3)$, then $f^{-1}(2)=\frac{3}{2}$.
Since the intersection point of the line $y=2$ and the graph of the function is $\left(\frac{3}{2}, 2\right)$, we have $f\left(\frac{3}{2}\right)=2$, and thus $f^{-1}(2)=\frac{3}{2}$.