已知函数y=f(x)在R上有……已知函数y=f(x)在R上有定义,当x>0时,f(x)>1,且对任意实数a,b,都有 f(a+b)=f(a)*f(b)恒成立.(1)求证:f(0)=1;(2)若f(x)*f(2x-x^2)>1,求x的取值范围;(3)证明:f(x)是R上的增函数.注意
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![已知函数y=f(x)在R上有……已知函数y=f(x)在R上有定义,当x>0时,f(x)>1,且对任意实数a,b,都有 f(a+b)=f(a)*f(b)恒成立.(1)求证:f(0)=1;(2)若f(x)*f(2x-x^2)>1,求x的取值范围;(3)证明:f(x)是R上的增函数.注意](/uploads/image/z/14389680-48-0.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0y%3Df%28x%29%E5%9C%A8R%E4%B8%8A%E6%9C%89%E2%80%A6%E2%80%A6%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0y%3Df%28x%29%E5%9C%A8R%E4%B8%8A%E6%9C%89%E5%AE%9A%E4%B9%89%2C%E5%BD%93x%3E0%E6%97%B6%2Cf%28x%29%3E1%2C%E4%B8%94%E5%AF%B9%E4%BB%BB%E6%84%8F%E5%AE%9E%E6%95%B0a%2Cb%2C%E9%83%BD%E6%9C%89+f%28a%2Bb%29%3Df%28a%29%2Af%28b%29%E6%81%92%E6%88%90%E7%AB%8B.%281%29%E6%B1%82%E8%AF%81%EF%BC%9Af%280%29%3D1%EF%BC%9B%282%29%E8%8B%A5f%28x%29%2Af%282x-x%5E2%29%3E1%2C%E6%B1%82x%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%EF%BC%9B%283%29%E8%AF%81%E6%98%8E%EF%BC%9Af%28x%29%E6%98%AFR%E4%B8%8A%E7%9A%84%E5%A2%9E%E5%87%BD%E6%95%B0.%E6%B3%A8%E6%84%8F)
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