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1. （5 分）已知集合 $A=\left\{x \mid x^{2}-2 x-3 \geqslant 0\right\}, B=\{x \mid-2 \leqslant x<2\}$, 则 $A \cap B=(\quad)$

Gaokao · Math · previous-year question

  1. A.$[1,2)$
  2. B.$[-1,1]$
  3. C.$[-1,2)$
  4. D.$[-2,-1]$correct

Answer

D. $[-2,-1]$

Explanation

解: 由 $\mathrm{A}$ 中不等式变形得: $(x-3)(x+1) \geqslant 0$, 解得: $x \geqslant 3$ 或 $x \leqslant-1$, 即 $A=(-\infty,-1] \cup[3,+\infty)$, $\because B=[-2,2)$, $\therefore A \cap B=[-2,-1]$. 故选：D.

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