2. The function $f(x)$ is undefined at $x=0$, but for all non-zero real numbers $x$, $f(x)+2 f\left(\frac{1}{x}\right)=3 x$. The solution situation for the equation $f(x)=f(-x)$ is
A. Exactly one real solution
B. Exactly two real solutions
C. No real solutions
D. Infinitely many, but not all non-zero real numbers
2. B Substitute $\frac{1}{x}$ into the equation, $f\left(\frac{1}{x}\right)+2 f(x)=\frac{3}{x}$, combining with the original equation we get, $f(x)=\frac{2-x^{2}}{x}$.