2. Let's define three functions, the first function is a monotonic function defined on the set of real numbers denoted as $y=f(x)$, its inverse function is the second function, and the third function is symmetrical to the second function about the line $x+y=0$. Then, the third function is ( ).
(A) $y=-f(x)$
(B) $y=-f(-x)$
(C) $y=-f^{-1}(x)$
(D) $y=-f^{-1}(-x)$
2. B.

Let $P(x, y)$ be any point on the third function, $Q_{1}\left(x_{1}, y_{1}\right)$ be the symmetric point of $P$ with respect to $x+y=0$, then $Q_{1}\left(x_{1}, y_{1}\right)$ is on the second function and $x_{1}=-y, y_{1}=-x$. Let $Q_{2}\left(x_{2}, y_{2}\right)$ be the symmetric point of $Q_{1}$ with respect to $x-y=0$, then $Q_{2}\left(x_{2}, y_{2}\right)$ is on the first function $y=f(x)$, and $x_{2}=y_{1}, y_{2}=x_{1} \Rightarrow x_{2}=-x, y_{2}=-y$, i.e., $y=-f(-x)$.