求函數(shù)y=(1/4)^X-(1/2)^X+1,x∈[-4,2]的單調(diào)區(qū)間及值域

數(shù)學(xué)人氣：667 ℃時(shí)間：2020-03-24 13:51:10

優(yōu)質(zhì)解答

以后記得要給分啊
設(shè) t=(1/2)^X => y=t^2 - t + 1 = (t-1/2)^2 + 3/4
x∈[-4,2] => t∈[1/4,16]且t=(1/2)^X是減函數(shù)
y在t=1/2最小為3/4 ；在t=16最大為241 故值域y∈[3/4,241]
t∈[1/4,1/2]時(shí)y= (t-1/2)^2 + 3/4是減函數(shù) 而t=(1/2)^X也是減函數(shù) 減減得增原函數(shù)曾單調(diào)增區(qū)間x∈[1,2]
t∈[1/2,16]時(shí)y= (t-1/2)^2 + 3/4是增函數(shù) 而t=(1/2)^X是減函數(shù) 增減得減原函數(shù)減單調(diào)減區(qū)間x∈[-4,1]