定義在[-2,2]上的偶函數(shù)g(x)滿足:當(dāng)x≥0時(shí),g(x)單調(diào)遞減.若g(1-m)<g(m),求m的取值范圍______.
∵定義在[-2,2]上的偶函數(shù)g(x)滿足:當(dāng)x≥0時(shí),g(x)單調(diào)遞減
∴偶函數(shù)g(x)在[-2,0]上是增函數(shù),在[0,2]上是減函數(shù),即自變量的絕對值越小,函數(shù)值越大
∵g(1-m)<g(m),
∴
| |1?m|>|m| | 1?m∈[?2,2] | m∈[?2,2] |
| |
,解得
,即-1≤m<
故答案為-1≤m<