Question

函数f(x) =sinx/根下（5+4cosx) （0≤x≤2π）的值域是

Answer 1

f(x)^2=(sinx)^2/（5+4cosx)=-0.25[(cosx)^2-1/(cosx+1.25)]

令a=cosx+1.25,所以a属于[0.25,1.25]

所以f(x)^2=-0.25[(x-1.25)^2-1/x]=-0.25(x+9/16x-2.5)

当且仅当x=0.75时x+9/16x有最小值,此时f(x)^2 max=0.25

f(x)^2 min=0

所以f(x)属于[-0.5,0.5]