f(x)=log1/2(x^2-2ax+3)说明a取何值时f(x)的值域为（-无穷,-1]

f(x)=log1/2(x^2-2ax+3)说明a取何值时f(x)的值域为（-无穷,-1]
f(x)=log1/2(x^2-2ax+3)说明a取何值时f(x)的值域为（-无穷,-1]

f(x)=log1/2(x^2-2ax+3)说明a取何值时f(x)的值域为（-无穷,-1]
若函数f(x)的值域为（-无穷,-1] ,由于0<1/2<0,等价于
x^2-2ax+3的最小值为2
令f=x^2-2ax+3=(x-a)^2+3-a^2
显然函数的最小值为3-a^2
故有3-a^2=2,得a=1或a=-1