1. Given the function $f(x)=|2 x-4|-3 x+8$ $(x \in \mathbf{R})$. Then the analytical expression of the inverse function $f^{-1}(x)$ is ( ).
(A) $f^{-1}(x)=-x+4(x \in \mathbf{R})$
(B) $f^{-1}(x)=-\frac{1}{5} x+\frac{12}{5}(x \in \mathbf{R})$
(C) $f^{-1}(x)=\left\{\begin{array}{l}-x+4, x \leqslant 2 ; \\ -\frac{1}{5} x+\frac{12}{5}, x>2\end{array}\right.$
(D) $f^{-1}(x)=\left\{\begin{array}{l}-\frac{1}{5} x+\frac{12}{5}, x<2 ; \\ -x+4, x \geqslant 2\end{array}\right.$
$$
-1 . \mathrm{C} .
$$

Because $f(x)=\left\{\begin{array}{l}-5 x+12, x2 .
\end{array}\right.$
$$