设函数的定义域为(0,+∞),且对任意的正实数x,y,有f(xy)=f(x)+f(y)恒成立,已知f(1/2)=1,且当x>1时,f(x)<0(1)求f(1)的值(2)证明:函数f(x)在(0,+∞)上是减函数,若f(x)+f(x-3/4)<2求实数x的取值范围.
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![设函数的定义域为(0,+∞),且对任意的正实数x,y,有f(xy)=f(x)+f(y)恒成立,已知f(1/2)=1,且当x>1时,f(x)<0(1)求f(1)的值(2)证明:函数f(x)在(0,+∞)上是减函数,若f(x)+f(x-3/4)<2求实数x的取值范围.](/uploads/image/z/3776881-49-1.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BA%280%2C%2B%E2%88%9E%EF%BC%89%2C%E4%B8%94%E5%AF%B9%E4%BB%BB%E6%84%8F%E7%9A%84%E6%AD%A3%E5%AE%9E%E6%95%B0x%2Cy%2C%E6%9C%89f%28xy%29%3Df%28x%29%2Bf%28y%29%E6%81%92%E6%88%90%E7%AB%8B%2C%E5%B7%B2%E7%9F%A5f%281%2F2%29%3D1%2C%E4%B8%94%E5%BD%93x%3E1%E6%97%B6%2Cf%28x%29%EF%BC%9C0%EF%BC%881%EF%BC%89%E6%B1%82f%281%29%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%E8%AF%81%E6%98%8E%EF%BC%9A%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8%EF%BC%880%2C%2B%E2%88%9E%EF%BC%89%E4%B8%8A%E6%98%AF%E5%87%8F%E5%87%BD%E6%95%B0%2C%E8%8B%A5f%28x%29%2Bf%28x-3%2F4%29%EF%BC%9C2%E6%B1%82%E5%AE%9E%E6%95%B0x%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.)
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