(A類)已知函數(shù)g(x)=(a+1)
x-2+1(a>0)的圖象恒過定點A,且點A又在函數(shù)f(x)=
log(x+a)的圖象上.
(1)求實數(shù)a的值; (2)解不等式f(x)<
loga;
(3)|g(x+2)-2|=2b有兩個不等實根時,求b的取值范圍.
(B類)設(shè)f(x)是定義在R上的函數(shù),對任意x,y∈R,恒有f(x+y)=f(x)+f(y)
(1)求f(0)的值; (2)求證:f(x)為奇函數(shù);
(3)若函數(shù)f(x)是R上的增函數(shù),已知f(1)=1,且f(2a)>f(a-1)+2,求a的取值范圍.