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. $y=-\varphi^{-1}(-x)$
The second function is $y=\varphi^{-1}(x)$, substituting $(-y,-x)$ for $(x, y) \Rightarrow -x=\varphi^{-1}(-y)$ $\Rightarrow -y=\varphi(-x) \Rightarrow y=-\varphi(-x)$ is the third function, so the answer is $B$.