若函数f(x)=根号【(a²-1)x²+(a-1)x+2/(a+1)】的定义域为R,求实数a的取值范

若函数f(x)=根号【(a²-1)x²+(a-1)x+2/(a+1)】的定义域为R,求实数a的取值范
若函数f(x)=根号【(a²-1)x²+(a-1)x+2/(a+1)】的定义域为R,求实数a的取值范

若函数f(x)=根号【(a²-1)x²+(a-1)x+2/(a+1)】的定义域为R,求实数a的取值范
定义域：(a²-1)x²+(a-1)x+2/(a+1)≥0,且a+1≠0
①a²-1=0,即a=1时,2/（1+1）=1≥0,恒成立
②a²-1＞0,即a＞1或a＜-1时,
△=(a-1)²-4(a²-1)×2/(a+1)≤0
得a²-10a+9≤0
(a-1)(a-9)≤0
解得1＜a≤9
综上：1≤a≤9
答案：1≤a≤9