已知函数 f(x)={aex−1,x≥0ae−x−1,x<0(a>0)f\left( x\right) = \left\{ \begin{array}{l} a{\mathrm{e}}^{x - 1},x \geq 0 \\ a{\mathrm{e}}^{-x - 1},x < 0 \end{array}\right. \left( {a > 0}\right)f(x)={aex−1,x≥0ae−x−1,x<0(a>0) ,若函数 f(x)f\left( x\right)f(x) 的图象上存在两个点 A(x1,y1),B(x2,y2)A\left( {{x}_{1},{y}_{1}}\right) ,B\left( {{x}_{2},{y}_{2}}\right)A(x1,y1),B(x2,y2) ,满足 y1y2−x1x2<0{y}_{1}{y}_{2} - {x}_{1}{x}_{2} < 0y1y2−x1x2<0 , 则 aaa 的取值范围为（ ）A. a≥2a \geq 2a≥2 B. a≥1a \geq 1a≥1 C. 0<a<10 < a < 10<a<1 D. 0<a<20 < a < 20<a<2