Question

已知集合A={x丨-2≤x≤a}，B={y丨y=2x+3，x∈A}，C={z丨z=x²，x∈A}，且B∪C=B，求a的取值范围。

告我思路。谢了

Answer 1

①若-2<=a<=0,C={x|a^2<=x<=4}
C是B的子集,有a^2>=-1,4<=2a+3, a无解
②若0<a<=2,C={x|0<=x<=4}
C是B的子集,有4<=2a+3, 解得1/2<=a<=2
③若a>2,C={0<=x<=a^2}
C是B的子集,有a^2<=2a+3, 解得2<a<=3
结合①②③得 1/2<=a<=3