已知函數(shù)f(x)=
,a為常數(shù)且a>0.
(1)證明:f(x)的圖象關(guān)于直線x=
對(duì)稱;
(2)若x
0滿足f(f(x
0))=x
0,但f(x
0)≠x
0,則x
0稱為函數(shù)f(x)的二階周期點(diǎn),如果f(x)有兩個(gè)二階周期點(diǎn)x
1,x
2,試確定a的取值范圍;
(3)對(duì)于(2)中的x
1,x
2,和a,設(shè)x
3為函數(shù)f(f(x))的最大值點(diǎn),A(x
1,f(f(x
1))),B(x
2,f(f(x
2))),C(x
3,0),記△ABC的面積為S(a),討論S(a)的單調(diào)性.