定义在正实数集上的函数f(x)满足下列条件(1)f(a)=1(a>1)(2)x属于正实数时,有f(x的m次方)=mf(x)(1)求证:f(xy)=f(x)+f(y);(2)证明:f(x)在正实数集上单调递增;(3)若不等式f(x)+f(4-x)
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![定义在正实数集上的函数f(x)满足下列条件(1)f(a)=1(a>1)(2)x属于正实数时,有f(x的m次方)=mf(x)(1)求证:f(xy)=f(x)+f(y);(2)证明:f(x)在正实数集上单调递增;(3)若不等式f(x)+f(4-x)](/uploads/image/z/935234-26-4.jpg?t=%E5%AE%9A%E4%B9%89%E5%9C%A8%E6%AD%A3%E5%AE%9E%E6%95%B0%E9%9B%86%E4%B8%8A%E7%9A%84%E5%87%BD%E6%95%B0f%28x%29%E6%BB%A1%E8%B6%B3%E4%B8%8B%E5%88%97%E6%9D%A1%E4%BB%B6%281%29f%28a%29%3D1%28a%3E1%29%282%29x%E5%B1%9E%E4%BA%8E%E6%AD%A3%E5%AE%9E%E6%95%B0%E6%97%B6%2C%E6%9C%89f%28x%E7%9A%84m%E6%AC%A1%E6%96%B9%29%3Dmf%28x%29%281%29%E6%B1%82%E8%AF%81%EF%BC%9Af%28xy%29%3Df%28x%29%2Bf%28y%29%3B%282%29%E8%AF%81%E6%98%8E%3Af%28x%29%E5%9C%A8%E6%AD%A3%E5%AE%9E%E6%95%B0%E9%9B%86%E4%B8%8A%E5%8D%95%E8%B0%83%E9%80%92%E5%A2%9E%EF%BC%9B%EF%BC%883%EF%BC%89%E8%8B%A5%E4%B8%8D%E7%AD%89%E5%BC%8Ff%28x%29%2Bf%284-x%29)
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定义在正实数集上的函数f(x)满足下列条件(1)f(a)=1(a>1)(2)x属于正实数时,有f(x的m次方)=mf(x)(1)求证:f(xy)=f(x)+f(y);(2)证明:f(x)在正实数集上单调递增;(3)若不等式f(x)+f(4-x)
定义在正实数集上的函数f(x)满足下列条件
(1)f(a)=1(a>1)
(2)x属于正实数时,有f(x的m次方)=mf(x)
(1)求证:f(xy)=f(x)+f(y);
(2)证明:f(x)在正实数集上单调递增;
(3)若不等式f(x)+f(4-x)<=2恒成立,求实数a的取值范围
定义在正实数集上的函数f(x)满足下列条件(1)f(a)=1(a>1)(2)x属于正实数时,有f(x的m次方)=mf(x)(1)求证:f(xy)=f(x)+f(y);(2)证明:f(x)在正实数集上单调递增;(3)若不等式f(x)+f(4-x)
解(1)设y=x^k
f(xy)=f(x^(k+1))=(k+1)f(x)=f(x)+kf(x)=f(x)+f(y)
得证
(2)设y>x y=xt t>1
f(y)-f(x)=f(xt)-f(x)
=f(x)+f(t)-f(x)=f(t)
因为t>1 所以f(t)>0
f(y)>f(x)所以单增
(3)f(x)+f(4-x)
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