這里x是指數(shù),可為任意數(shù),即x屬于R
f(x)=-(1/4)^x+4(1/2)^x+5=-[(1/2)^x]^2+4(1/2)^x+5
令(1/2)^x=t,t≥0
f(x)=-t^2+4t+5=-(t-2)^2+9≤9
t為單調(diào)遞減函數(shù),而當(dāng)t≥2時(shí),f(x)為單調(diào)遞減,即x≤-1
當(dāng)t-1
由同增異減可知：x≤-1時(shí)為增函數(shù),x>-1時(shí)為減函數(shù)
所以：定義域?yàn)镽,值域?yàn)椤?∞,1】
單調(diào)遞減區(qū)間為【-1,+ ∞】,單調(diào)遞增區(qū)間為【-∞,-1】