3. The graph of the function $y=f(x)$ consists of two segments of a circle with the origin as the center and a radius of 1, as shown in Figure 6-1. Then the solution set of the inequality $f(x) > f(-x) + x$ is $(\quad)$.
A. $\left[-1,-\frac{2 \sqrt{5}}{5}\right) \cup(0,1]$
B. $[-1,0) \cup\left(0, \frac{2 \sqrt{5}}{5}\right)$
C. $\left[-1,-\frac{2 \sqrt{5}}{5}\right) \cup\left(0, \frac{2 \sqrt{5}}{5}\right)$
D. $\left[-1,-\frac{2 \sqrt{5}}{5}\right) \cup\left(\frac{2 \sqrt{5}}{5}, 1\right]$