1. If the graph of the function $f(x)$ is a broken line connecting the points $(0,0),(1,1)$, and $(2,3)$ in sequence, then $f^{-1}(2)$ $=$.
According to the problem, $f(x)$ is a monotonically increasing function, and the midpoint of the line segment connecting the points $(1,1),(2,3)$ is $\left(\frac{3}{2}, 2\right)$, so $f^{-1}(2)=\frac{3}{2}$.