$7 \cdot 80$ 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) $y=-\varphi^{-1}(-x)$.
[Solution] The second function is $y=\varphi^{-1}(x)$. From the graph, it is easy to see that the third function is centrally symmetric to the first function with respect to the origin.
That is,
$$
y=-\varphi(-x) .
$$

Therefore, the answer is (B).