y=(1/4)的x次方-(1/2)的x次方+1x∈[-3,2]求y的单调区间和值域怎么通过x的取值求t的取值

Question

y=(1/4)的x次方-(1/2)的x次方+1
x∈[-3,2]求y的单调区间和值域
怎么通过x的取值求t的取值

Answer 1

y=(1/4)^x-(1/2)^x+1
=(1/2)^2x-(1/2)^x+1
t=(1/2)^x
x∈[-3,2],t∈[1/4,8]
y=t^2-t+1
t=1/2 x=1 ymin=3/4
t=8 x=-3 ymax=57
y∈[3/4,57]
单调增区间(1,2]
单调减区间[-3,1)