1. Given the function $y=-\frac{x-a}{x-a-1}$, the graph of its inverse function is symmetric with respect to the point $(-1,3)$. Then the real number $a$ equals ( ).
(A) 2
(B) 3
(C) -2
(D) -4
-1. (A).
From the problem, we know that the graph of the function $y=-\frac{x-a}{x-a-1}$ is centrally symmetric about the point (3, 1). By $y=-\frac{x-a}{x-a-1}=-1-\frac{1}{x-a-1}$, we get: $(x-a-1)(y+1)=-1$, which is a hyperbola centered at the point $(a+1,-1)$. Therefore, $a+1=3$, which means $a=2$.