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](/uploads/image/z/3775416-24-6.jpg?t=%E6%B1%82%E5%87%BD%E6%95%B0y%3D%EF%BC%881%2F4%EF%BC%89x%E6%96%B9-%EF%BC%881%2F2%EF%BC%89x%E6%96%B9%2B1+%EF%BC%88x%E5%B1%9E%E4%BA%8E%E3%80%90-3%2C2%E3%80%91%EF%BC%89%E7%9A%84%E5%80%BC%E5%9F%9F)
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]