Question

函數(shù)f（x）=（m²-m-1）x^m是冪函數(shù)，則實數(shù)m的值為

-1或2

．

Answer 1

分析：因為只有y=x^α型的函數(shù)才是冪函數(shù)，所以只有m²-m-1=1函數(shù)f（x）=（m²-m-1）x^m才是冪函數(shù)，據(jù)此得出答案．

解答：解：要使函數(shù)f（x）=（m²-m-1）x^m是冪函數(shù)，
則 m²-m-1=1
解得：m=-1或2．
故答案為：-1或2．

點(diǎn)評：本題考查了冪函數(shù)的概念及其單調(diào)性，解答的關(guān)鍵是掌握冪函數(shù)定義及性質(zhì)．