1.對于定義在R上的函數(shù)y=f(x)和y=g(x),若對任意給定的x
1,x
2∈R,不等式|f(x
1)-f(x
2)|≥|g(x
1)-g(x
2)|都成立,則稱函數(shù)y=g(x)是函數(shù)y=f(x)的“從屬函數(shù)”
(1)若函數(shù)y=g(x)是函數(shù)y=f(x)的“從屬函數(shù)”,且y=f(x)是偶函數(shù),求證:y=g(x)是偶函數(shù)
(2)設
.求證:當a≥1時,函數(shù)y=g(x)是函數(shù)y=f(x)的“從屬函數(shù)”;
(3)若定義在R上的函數(shù)y=f(x)和y=g(x)的圖像均為一條連續(xù)曲線,且函數(shù)y=g(x)是函數(shù)y=f(x)的“從屬函數(shù)”,求證:“函數(shù)y=f(x)在R上是嚴格增函數(shù)或嚴格減函數(shù)”是“函數(shù)y=g(x)在R上是嚴格增函數(shù)或嚴格減函數(shù)”的必要非充分條件.