设函数f(x)的定义域为(0,+∞),且对任意实数x,y,有f(xy)=f(x)+f(y),已知f(2)=1,且设函数f(x)的定义域为(0,+∞),且对任意实数x,y,有f(xy)=f(x)+f(y),已知f(2)=1,且当x>1时,f(x)>0,求证f(1/2)=-1
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![设函数f(x)的定义域为(0,+∞),且对任意实数x,y,有f(xy)=f(x)+f(y),已知f(2)=1,且设函数f(x)的定义域为(0,+∞),且对任意实数x,y,有f(xy)=f(x)+f(y),已知f(2)=1,且当x>1时,f(x)>0,求证f(1/2)=-1](/uploads/image/z/3017967-15-7.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BA%280%2C%2B%E2%88%9E%29%2C%E4%B8%94%E5%AF%B9%E4%BB%BB%E6%84%8F%E5%AE%9E%E6%95%B0x%2Cy%2C%E6%9C%89f%28xy%29%3Df%28x%29%2Bf%28y%29%2C%E5%B7%B2%E7%9F%A5f%282%29%3D1%2C%E4%B8%94%E8%AE%BE%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BA%280%EF%BC%8C%2B%E2%88%9E%29%2C%E4%B8%94%E5%AF%B9%E4%BB%BB%E6%84%8F%E5%AE%9E%E6%95%B0x%2Cy%2C%E6%9C%89f%EF%BC%88xy%EF%BC%89%3Df%EF%BC%88x%EF%BC%89%2Bf%EF%BC%88y%EF%BC%89%2C%E5%B7%B2%E7%9F%A5f%EF%BC%882%EF%BC%89%3D1%2C%E4%B8%94%E5%BD%93x%3E1%E6%97%B6%2Cf%28x%29%3E0%EF%BC%8C%E6%B1%82%E8%AF%81f%EF%BC%881%2F2%EF%BC%89%3D-1)
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