已知函數(shù)f(x)的定義域是(0,正無窮),當(dāng)x>1時(shí),f(x)
已知函數(shù)f(x)的定義域是(0,正無窮),當(dāng)x>1時(shí),f(x)<0,且f(x*y)=f(x)+f(y) 1.證明f(x)在定義域上是減函數(shù)
2.如果f(3分之根號(hào)3)=1,求滿足不等式f(x)-f(1/X-2)>等于-2的x的取值范圍
其他人氣:778 ℃時(shí)間:2019-08-19 13:02:53
優(yōu)質(zhì)解答
1.0f(t)- f(u)
f(u*t/u)-f(u)
=f(u)+f(t/u)-f(u)
=f(t/u)<0(t/u>1)
f(t)f(x)在定義域上是減函數(shù)
2.
x>2
f(x)-f(1/(x-2)) ≥-2
f(1/(x-2)) ≤2+ f(x)
=f(√3/3)+ f(√3/3)+ f(x)
=f(1/3)+f(x)
=f(x/3)
f(x)在定義域上是減函數(shù)
1/(x-2) ≥x/3
2