Question

求函数Y=(1/4)^X+(1/2)^X+1值域

Answer 1

y=(1/4)^x+(1/2)^x+1

=[(1/2)^x] ² +(1/2)^x+1

=[(1/2)^x+1/2] ²+3/4

因为(1/2)^x＞0

故：(1/2)^x+1/2＞1/2

故：[(1/2)^x+1/2] ²＞1/4

故：y=[(1/2)^x+1/2] ²+3/4＞1

即：值域为(1,+∞)