Question

若A={x|-2≤x≤a},B={y|y=2x+3,x∈A},C={z|z=x^2,x∈A},若C包含与B，试求a的值?

Answer 1

-2≤x≤a
-4≤2x≤2a
-1≤2x+3≤2a+3
所以B={y|y=2x+3,-1≤2x+3≤2a+3}
对z来说，下限已经在B之内，需要对上限进行限制
-2≤x≤a
0<=x^2<=4和a^2当中较大的那个
下列不等式必须同时满足
a^2<=2a+3
a^2<=4
(a-3)(a+1)<=0,-1<=a<=3
-2<=a<=2
所以a的取值为
-1<=a<=2