(文) 若实数x满足对任意正数a>0,均有x2<1+a,则x的取值范围是_.

问题描述:

(文) 若实数x满足对任意正数a>0,均有x2<1+a,则x的取值范围是______.

实数x满足对任意正数a>0,均有x2<1+a
令f(a)=a+1-x2,a>0则由一次函数的性质可得f(0)=1-x2≥0
-1≤x≤1
故答案为:[-1,1]