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. Hint: From $y=f^{\prime 1}(-x)$, we get $f(y)=-x$, so $y=-f(x)$ is the inverse function of $y=f^{-1}(-x)$, i.e., $-f(x)=$ $f(-x)$, which shows that $y=f(x)$ is an odd function.