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
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![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](/uploads/image/z/1265799-39-9.jpg?t=%E8%8B%A5%E5%87%BD%E6%95%B0f%28x%29%3D%E6%A0%B9%E5%8F%B7%E3%80%90%28a%26%23178%3B-1%29x%26%23178%3B%2B%28a-1%29x%2B2%2F%28a%2B1%29%E3%80%91%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BAR%2C%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83)
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