已知定义在[-1,1]上的单调函数f(x)满足f(1/3)=log底2真数3,且对于任意的x∈[-1,1]都有f(x+y)=f(x)+f(y)(1)求证:f(x)为奇函数(2)试求使f(1-m)+f(1-2m)<0成立的m的取值范围
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![已知定义在[-1,1]上的单调函数f(x)满足f(1/3)=log底2真数3,且对于任意的x∈[-1,1]都有f(x+y)=f(x)+f(y)(1)求证:f(x)为奇函数(2)试求使f(1-m)+f(1-2m)<0成立的m的取值范围](/uploads/image/z/1003115-11-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9A%E4%B9%89%E5%9C%A8%5B-1%2C1%5D%E4%B8%8A%E7%9A%84%E5%8D%95%E8%B0%83%E5%87%BD%E6%95%B0f%28x%29%E6%BB%A1%E8%B6%B3f%281%2F3%29%3Dlog%E5%BA%952%E7%9C%9F%E6%95%B03%2C%E4%B8%94%E5%AF%B9%E4%BA%8E%E4%BB%BB%E6%84%8F%E7%9A%84x%E2%88%88%5B-1%2C1%5D%E9%83%BD%E6%9C%89f%EF%BC%88x%2By%EF%BC%89%3Df%EF%BC%88x%EF%BC%89%2Bf%EF%BC%88y%EF%BC%89%EF%BC%881%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9Af%EF%BC%88x%EF%BC%89%E4%B8%BA%E5%A5%87%E5%87%BD%E6%95%B0%EF%BC%882%EF%BC%89%E8%AF%95%E6%B1%82%E4%BD%BFf%EF%BC%881-m%EF%BC%89%2Bf%EF%BC%881-2m%EF%BC%89%EF%BC%9C0%E6%88%90%E7%AB%8B%E7%9A%84m%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
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