中难度的函数题,定义在R上的函数y=f(x),f(0)不等于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)证明f(x)是R的增函数
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![中难度的函数题,定义在R上的函数y=f(x),f(0)不等于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)证明f(x)是R的增函数](/uploads/image/z/14650230-30-0.jpg?t=%E4%B8%AD%E9%9A%BE%E5%BA%A6%E7%9A%84%E5%87%BD%E6%95%B0%E9%A2%98%2C%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%E4%B8%8D%E7%AD%89%E4%BA%8E0%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%E7%9A%84a.b%26%238364%3BR%2C%E6%9C%89f%28a%2Bb%29%3Df%28a%29f%28b%29%EF%BC%881%EF%BC%89%E6%B1%82%E8%AF%81f%280%29%3D1%EF%BC%882%EF%BC%89%E6%B1%82%E8%AF%81%E5%AF%B9%E4%BB%BB%E6%84%8F%E7%9A%84x%26%238364%3BR%2C%E6%81%92%E6%9C%89f%28x%29%3E0%EF%BC%883%EF%BC%89%E8%AF%81%E6%98%8Ef%28x%29%E6%98%AFR%E7%9A%84%E5%A2%9E%E5%87%BD%E6%95%B0)
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