$30 n$ 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