求函数y=(1/4)x方-(1/2)x方+1 (x属于【-3,2】)的值域
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求函数y=(1/4)x方-(1/2)x方+1(x属于【-3,2】)的值域求函数y=(1/4)x方-(1/2)x方+1(x属于【-3,2】)的值域求函数y=(1/4)x方-(1/2)x方+1(x属于【-
求函数y=(1/4)x方-(1/2)x方+1 (x属于【-3,2】)的值域
求函数y=(1/4)x方-(1/2)x方+1 (x属于【-3,2】)的值域
求函数y=(1/4)x方-(1/2)x方+1 (x属于【-3,2】)的值域
令y=(1/2)^x=t
∵-3≤x≤2,∴(1/2)^2≤(1/2)^x≤(1/2)^(-3)
∴(1/4)≤t≤8
则y=t^2-t+1=(t-1/2)^2+(3/4) (t∈[1/4,8]
∴当t=1/2时,y最小值=3/4
当t=8时,y最大值=57
∴原函数值域为[3/4,57]