1. Suppose there are three functions, the first one is $y=\varphi(x)$, its inverse function is the second function, and the graph of the third function is symmetric to the graph of the second function about the line $x+y=0$, then the third function is
(A) $y=-\varphi(x)$;
(B) $y=-\varphi(-x)$;
(C) $y=-\varphi^{-1}(x)$;
(D) $y=-\varphi^{-1}(-x)$.
Answer ( )
1. (B)

The graph of the first function is symmetric to the graph of the second function with respect to $x-y=0$. The graph of the second function is symmetric to the graph of the third function with respect to $x+y=0$, so the graph of the first function is symmetric to the graph of the third function with respect to the origin.