已知f(x)是定义在R上的恒不为零的函数,且对于任意的x,y∈R都有f(x+y)=xf(y)+yf(x)(1)求f(0)f(1)的值(2)判断其奇偶性(3)若f(x)在【0,无限大)上是增函数且f(x)+f(x-1|2)小于0求x范围
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![已知f(x)是定义在R上的恒不为零的函数,且对于任意的x,y∈R都有f(x+y)=xf(y)+yf(x)(1)求f(0)f(1)的值(2)判断其奇偶性(3)若f(x)在【0,无限大)上是增函数且f(x)+f(x-1|2)小于0求x范围](/uploads/image/z/7243394-50-4.jpg?t=%E5%B7%B2%E7%9F%A5f%28x%29%E6%98%AF%E5%AE%9A%E4%B9%89%E5%9C%A8R%E4%B8%8A%E7%9A%84%E6%81%92%E4%B8%8D%E4%B8%BA%E9%9B%B6%E7%9A%84%E5%87%BD%E6%95%B0%2C%E4%B8%94%E5%AF%B9%E4%BA%8E%E4%BB%BB%E6%84%8F%E7%9A%84x%2Cy%E2%88%88R%E9%83%BD%E6%9C%89f%28x%2By%29%3Dxf%28y%29%2Byf%28x%29%281%29%E6%B1%82f%280%29f%281%29%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%E5%88%A4%E6%96%AD%E5%85%B6%E5%A5%87%E5%81%B6%E6%80%A7%EF%BC%883%EF%BC%89%E8%8B%A5f%EF%BC%88x%EF%BC%89%E5%9C%A8%E3%80%900%2C%E6%97%A0%E9%99%90%E5%A4%A7%EF%BC%89%E4%B8%8A%E6%98%AF%E5%A2%9E%E5%87%BD%E6%95%B0%E4%B8%94f%EF%BC%88x%EF%BC%89%2Bf%EF%BC%88x-1%7C2%EF%BC%89%E5%B0%8F%E4%BA%8E0%E6%B1%82x%E8%8C%83%E5%9B%B4)
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