我們知道,函數(shù)y=f(x)的圖象關(guān)于y軸成軸對(duì)稱(chēng)圖形的充要條件是函數(shù)y=f(x)為偶函數(shù),有同學(xué)發(fā)現(xiàn)可以將其推廣為:函數(shù)y=f(x)的圖象關(guān)于x=a成軸對(duì)稱(chēng)圖形的充要條件是函數(shù)y=f(x+a)為偶函數(shù).
(1)已知函數(shù)φ(x)=x
2-2x+a(e
x-1+e
-x+1),求該函數(shù)圖象的對(duì)稱(chēng)軸方程;
(2)若函數(shù)g(x)的圖象關(guān)于直線(xiàn)x=1對(duì)稱(chēng),且當(dāng)x≥1時(shí),g(x)=x
2-
.
①求g(x)的解析式;
②求不等式g(x)>g(3x-1)的解集.