f(x)=(1/3)^x ,x∈(-1,1)
∴f(x)∈(1/3,3)
令t=f(x)∈(1/3,3)
∴g(t)=t²-2at+3
g(t)对称轴是t=a
(1)当a＞3时,g(t)min=g(3)=9-6a+3=12-6a
(2)当a＜1/3时,g(t)min=g(1/3)=1/9 -(2/3)a+3=28/9 -(2/3)a
(3)当a∈[1/3,3]时,g(t)min=g(a)=a²-2a²+3=3-a²
综上,
当a＞3时,h(a)=12-6a
当a＜1/3时,h(a)=28/9 -(2/3)a
当a∈[1/3,3]时,h(a)=3-a²
谢谢