Question

若函數(shù)f(x)=lg(x²+ax-a-1)在區(qū)間［2,+∞)上單調(diào)遞增,則實(shí)數(shù)a的取值范圍是_________.

Answer 1

解析:本題考查復(fù)合函數(shù)單調(diào)性的判定方法,要注意判斷函數(shù)的單調(diào)性必須在函數(shù)的定義域內(nèi)進(jìn)行.

∵函數(shù)f(x)在區(qū)間［2,+∞)上單調(diào)遞增,

∴-≤2,且x=2時(shí),x²+ax-a-1＞0,即

∴a＞-3,即實(shí)數(shù)a的取值范圍是(-3,+∞).

答案:(-3,+∞).