3. The function $f(x)=\frac{x}{1-2^{x}}-\frac{x}{2}$
A. is an even function but not an odd function
B. is an odd function but not an even function
C. is both an odd and an even function
D. is neither an odd nor an even function
3. $\mathrm{A}$

The domain is $(-\infty, 0) \cup(0,+\infty) \cdot f(-x)=\frac{-x}{1-2^{-x}}-\frac{-x}{2}=\frac{x+x\left(2^{x}-1\right)}{1-2^{x}}+\frac{x}{2}=\frac{x}{1-2^{x}}-x+$ $\frac{x}{2}=\frac{x}{1-2^{x}}-\frac{x}{2}=f(x)$.