Question

y=(cosx +1)/(cosx+3)求值域

Answer 1

1.设u=cosx+3,则u∈[2,4],

y=(u-2)/u=1-2/u是u的增函数,

∴y的值域是[0,1/2].

2.x∈[π/3,5π/4],

∴u=cosx的值域是[-1,1/2],

∴y=-u-1的值域是[-3/2,0].

3.0≤θ≤π/3,

∴1/2≤cosθ≤1,

∴a的取值范围是[-1/2,0].