Question

求f(x)=4^(x-1/2)-3*2^x+5的值域 x:[0,2]

Answer 1

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]