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Gaokao Math Practice Question

已知函数 $\left\{\begin{array}{l}e^{x}, x \leqslant 0, \\ ln x, x>0 \end{array}, g(x)=f(x)+x+a \right.$.若 $g(x)$ 存在 $2$ 个零点, 则 $a$ 的取值范围是 ($\qquad$)

  1. A.$[-1,0)$
  2. B.$[0,+\infty)$
  3. C.$[-1,+\infty)$
  4. D.$[1,+\infty)$

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