f(x)是定义域在正实数的递增函数,且f(xy)=f(x)+f(y),求证:f(x/y)=f(x)+f(y)(2):若F(3)=1且f(a)>f(a-1)+2,求a的取值范围是的是的,应该是-
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![f(x)是定义域在正实数的递增函数,且f(xy)=f(x)+f(y),求证:f(x/y)=f(x)+f(y)(2):若F(3)=1且f(a)>f(a-1)+2,求a的取值范围是的是的,应该是-](/uploads/image/z/1996912-64-2.jpg?t=f%28x%29%E6%98%AF%E5%AE%9A%E4%B9%89%E5%9F%9F%E5%9C%A8%E6%AD%A3%E5%AE%9E%E6%95%B0%E7%9A%84%E9%80%92%E5%A2%9E%E5%87%BD%E6%95%B0%2C%E4%B8%94f%28xy%29%3Df%28x%29%2Bf%28y%29%2C%E6%B1%82%E8%AF%81%EF%BC%9Af%28x%2Fy%29%3Df%28x%29%2Bf%28y%29%282%29%3A%E8%8B%A5F%283%29%3D1%E4%B8%94f%28a%29%EF%BC%9Ef%28a-1%29%2B2%2C%E6%B1%82a%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E6%98%AF%E7%9A%84%E6%98%AF%E7%9A%84%EF%BC%8C%E5%BA%94%E8%AF%A5%E6%98%AF-)
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f(x)是定义域在正实数的递增函数,且f(xy)=f(x)+f(y),求证:f(x/y)=f(x)+f(y)(2):若F(3)=1且f(a)>f(a-1)+2,求a的取值范围是的是的,应该是-
f(x)是定义域在正实数的递增函数,且f(xy)=f(x)+f(y),求证:f(x/y)=f(x)+f(y)
(2):若F(3)=1且f(a)>f(a-1)+2,求a的取值范围
是的是的,应该是-
f(x)是定义域在正实数的递增函数,且f(xy)=f(x)+f(y),求证:f(x/y)=f(x)+f(y)(2):若F(3)=1且f(a)>f(a-1)+2,求a的取值范围是的是的,应该是-
首先,我觉得你可能打错题了,以我做题的经验,应该是求证f(x/y)=f(x)—f(y)吧,然后,不管第一问怎样,第二问都能解出来,我就按“-”求证吧
注:x^2=x*x(x的平方)
(1)f(x/y)=f(x)+f(1/y).
由f(xy)=f(x)+f(y)得f(xy)-f(y)=f(x),令x=y^2,y=1/y(y>0),则f(y)-f(1/y)=f(y^2)=f(y*y)=f(y)+f(y)
合并同类项,得f(1/y)=-f(y),代入上式,得f(x/y)=f(x)-f(y)
(2)2=1+1=f(3)+f(3)=f(9),f(9)+f(a-1)=f(9a-9),因为f(x)是定义域在正实数的递增函数,所以由f(a)>f(a-1)+2得a>0,a-1>0,a>9a-9,解得
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