$30 n$ is a fixed integer. The function $f(x)=x^{n}$ has the property: $f_{(1)}^{2}+f_{(-1)}^{2}=2[f(1)+f(-1)-1]$, then the function $f(x)$
A. is an odd function
B. is an even function
C. is both an odd and an even function
D. is neither an odd nor an even function
30 B. From $f^{2}(1)+f^{2}(-1)=2 f(1)+2 f(-1)-2$, we get $[f(1)-1]^{2}+[f(-1)-1]^{2}$ $=0$, so $f(1)=1, f(-1)=1$. This indicates that $n$ is even, hence the power function $f(x)$ is an even function.