已知x≥0,y≥0,x+y=1,求函数u=log1/2(8xy+4y2+1)的值域

8xy+4y^2+1=4x^2+8xy+4y^2+1-4x^2=4(x+y)^2+1-4x^2(因x+y=1)=5-4x^2.易知,0《x《1===>1《5-4x^2《5.即1《8xy+4y^2+1《5.====>log(1/2)1》》log(1/2)5.===>-log(2)5《log(1/2)[8xy+4y^2+1]《0.====>-log(2)5《u《0.