f（2的X次方）的定义域是【-1，1】即-1<=x<=1所以2^-1<=2^x<=2^1所以f(x)定义域是1/2<=x<=2所以f(log2(x))中1/2<=log2(x)<=22^(1/2)<=2^log2(x)<=2^22^(1/2)<=x<=4所以定义域[根号2，4]
根据题意2^x∈(1,2)，所以x∈(0,1)f(2^x)的定义域为(0,1)
(0,1)
