如图,函数y=f(x)的图像是中心在原点,焦点在x轴上的椭圆的两段弧,则不等式f(x)<f(-x)+x的解集为 (     )

A：$(-\sqrt{2},0)\cup (\sqrt{2},2$

B：$-2,-\sqrt{2})\cup (\sqrt{2},2$

C：$-2,-\frac{\sqrt{2}}{2})\cup (\frac{\sqrt{2}}{2},2$

D：$\left(-\sqrt{2},0\right)\cup \left(0,\sqrt{2}\right)$