Question

求函数y=(2/3)^(-x^2+3x-1/4)的值域

Answer 1

设t=-x^2+3x-1/4,

t=-x^2+3x-1/4=-(x-3/2)^2+2

因为-(x-3/2)^2≤0,所以-(x-3/2)^2+2≤2.

y=(2/3)^t是减函数,

所以(2/3)^t≥(2/3)^2=4/9,

函数值域是[4/9,+∞）.