f(x)=4^(x-1/2)-3*2^x+5
= 4^x/2-3*2^x+5
=((2^x)^2-6*2^x+9)/2+1/2
=(2^x-3)^2/2+1/2
2^x=3时,f(x)最小=1/2
x=0,2^x=1时,f(x)最大=5/2
值域：[1/2,5/2]