定义在R上的函数y=f(x),f(0)≠0,当x>0时,f(x)>1,且对任意的a,b∈R,有f(a+b)=f(a)f(b)(1)求证:f(0)=1(2)求证:对任意的x∈R,恒有f(x)>0(3)求证f(x)是R上的增函数(4)若f(x)f(2x-x^2)>1,求x的取值范围
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![定义在R上的函数y=f(x),f(0)≠0,当x>0时,f(x)>1,且对任意的a,b∈R,有f(a+b)=f(a)f(b)(1)求证:f(0)=1(2)求证:对任意的x∈R,恒有f(x)>0(3)求证f(x)是R上的增函数(4)若f(x)f(2x-x^2)>1,求x的取值范围](/uploads/image/z/2428688-56-8.jpg?t=%E5%AE%9A%E4%B9%89%E5%9C%A8R%E4%B8%8A%E7%9A%84%E5%87%BD%E6%95%B0y%3Df%28x%29%2Cf%280%29%E2%89%A00%2C%E5%BD%93x%EF%BC%9E0%E6%97%B6%2Cf%28x%29%EF%BC%9E1%2C%E4%B8%94%E5%AF%B9%E4%BB%BB%E6%84%8F%E7%9A%84a%2Cb%E2%88%88R%2C%E6%9C%89f%28a%2Bb%29%3Df%28a%29f%28b%29%EF%BC%881%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9Af%280%29%3D1%282%29%E6%B1%82%E8%AF%81%3A%E5%AF%B9%E4%BB%BB%E6%84%8F%E7%9A%84x%E2%88%88R%2C%E6%81%92%E6%9C%89f%28x%29%EF%BC%9E0%283%29%E6%B1%82%E8%AF%81f%28x%29%E6%98%AFR%E4%B8%8A%E7%9A%84%E5%A2%9E%E5%87%BD%E6%95%B0%EF%BC%884%EF%BC%89%E8%8B%A5f%28x%29f%282x-x%5E2%29%3E1%2C%E6%B1%82x%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
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