對于函數(shù)y=f(x),若實數(shù)x
0滿足f(x
0)f(x
0+F)=D,其中F、D為實數(shù),則x
0稱為函數(shù)f(x)的“F-D-篤志點”.
(1)若f(x)=x+1,求函數(shù)f(x)的“1-2-篤志點”;
(2)已知函數(shù)
,且函數(shù)f(x)有且只有3個“1-1-篤志點”,求實數(shù)a的取值范圍;
(3)定義在R上的函數(shù)f(x)滿足:存在唯一實數(shù)m,對任意的實數(shù)x,使得f(m+x)=f(m-x)恒成立或f(m+x)=-f(m-x)恒成立.對于有序?qū)崝?shù)對(F,D),討論函數(shù)f(x)“F-D-篤志點”個數(shù)的奇偶性,并說明理由.