设函数f(x)=2log2x-log2(x-1),则f(x)的定义域为_,f(x)的最小值为__.
问题描述:
设函数f(x)=2log2x-log2(x-1),则f(x)的定义域为_,f(x)的最小值为__.
答
x-1>0 ∴x>1 ∴f(x)的定义域为x>1f(x)=2log2x-log2(x-1)=㏒2x²-㏒2(x-1)=㏒2[x²/(x-1)]x²/(x-1)=(x²-1)/(x-1)+1/(x-1)=x+1+1/(x-1)=(x-1)+1/(x-1)+2≥3³√2∴f(x)...