已知函数f(x)=log^2以0.5为底x的对数 - 2log以0.5为底x的对数 + 3
(1)若x∈[1/4 ,2] ,求函数f(x)的值
(2)求不等式f(x)≥6的解集
(1)解析：∵函数f(x)=(log(0.5,x))^2-2log(0.5,x)+3
令f’(x)=[2log(0.5,x)-2]/(xln0.5)=0==>x=0.5
f”(x)=1/ln0.5*[2/ln0.5-2log(0.5,x)+2] /(x)^2
f”(0.5)=8/(ln0.5)^2>0
∴函数f(x)在x=0.5处取极小值；
∵x∈[1/4 ,2]
f(1/4)=4-4+3=3
f(1/2)=1-2+3=2
f(2)=1+2+3=6
∴函数f(x)的值域为[2,6]
(2)解析：f(x)=(log(0.5,x))^2-2log(0.5,x)+3>=6
log(0.5,x)x>=2
log(0.5,x)>=3==>0