1. The inverse function of the function $y=f(-x)$ defined on the set of real numbers $\mathbf{R}$ is $y=f^{-1}(-x)$, then ( ).
(A) $y=f(x)$ is an odd function
(B) $y=f(x)$ is an even function
(C) $y=f(x)$ is both an odd and an even function
(D) $y=f(x)$ is neither an odd nor an even function
-1 (A).
From $y=f^{-1}(-x)$, we get $f(y)=-x$. Therefore, $y=-f(x)$ is the inverse function of $y=f^{-1}(-x)$, i.e., $-f(x)=f(-x)$.
This shows that $y=f(x)$ is an odd function.