Question

冪函數(shù)y=(m2-m-1)xm2-2m-3在[0，+∞）上是單調(diào)遞減的函數(shù)，則實(shí)數(shù)m的值為

2

．

Answer 1

分析：由題意冪函數(shù)y=(m2-m-1)xm2-2m-3在[0，+∞）上是單調(diào)遞減的函數(shù)，由此可得

m2-m-1=1 m2-2m-3＜0

解此不等式組即可求出實(shí)數(shù)m的值

解答：解：冪函數(shù)y=(m2-m-1)xm2-2m-3在[0，+∞）上是單調(diào)遞減的函數(shù)
∴

m2-m-1=1 m2-2m-3＜0

解得m=2
故答案為2

點(diǎn)評(píng)：本題考點(diǎn)是冪函數(shù)的單調(diào)性，奇偶性及其應(yīng)用，考察了冪函數(shù)的定義，冪函數(shù)單調(diào)性與指數(shù)的對(duì)應(yīng)關(guān)系，解題的關(guān)鍵是理解冪函數(shù)的定義及冪函數(shù)的單調(diào)性與指數(shù)的對(duì)應(yīng)關(guān)系，本題是冪函數(shù)的基礎(chǔ)題，考察了推理判斷的能力