7. The range of the function $f(x)$ $=\frac{x-x^{3}}{\left(1+x^{2}\right)^{2}}$ is $\qquad$ _.
$$
f(x)=\frac{x-x^{3}}{\left(1+x^{2}\right)^{2}}=\frac{1}{2} \cdot \frac{2 x}{1+x^{2}} \cdot \frac{1-x^{2}}{1+x^{2}} \xlongequal{x=\tan \frac{\alpha}{2}} \frac{1}{2} \sin \alpha \cos \alpha=\frac{1}{4} \sin 2 \alpha,
$$

Therefore, the range of the function $f(x)$ is $\left[-\frac{1}{4}, \frac{1}{4}\right]$.