Question

求函数f(x)=2sin(2x-π/3)的值域（6/π

Answer 1

6/π≤x≤2π/3?应该是π/6≤x≤2π/3吧?

如果是的话,

令y=2x-π/3,则：f(y)=2siny

此时：x=y/2-π/6,

当x∈[π/6,2π/3],有：y∈[0,π]

对于f(y)=2siny,当y∈[0,π]时,有：f(y)∈[0,1]

所以,对于f(x)=sin(2x-π/3),当x∈[π/6,2π/3]时,有：f(x)∈[0,1]

即所求值域是：0≤f(x)≤1.