高一函数题,已知函数f(x)的定义域是x属于R且x≠0,对定义域内的任意x1、x2都有f(x1·x2)=f(x1)+f(x2)且当x>1时f(x)>0,f(2)=1(1)求证:f(x)是偶函数(2)求证:f(x)在(0,正无穷)上是增函数(3)解
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![高一函数题,已知函数f(x)的定义域是x属于R且x≠0,对定义域内的任意x1、x2都有f(x1·x2)=f(x1)+f(x2)且当x>1时f(x)>0,f(2)=1(1)求证:f(x)是偶函数(2)求证:f(x)在(0,正无穷)上是增函数(3)解](/uploads/image/z/12921605-53-5.jpg?t=%E9%AB%98%E4%B8%80%E5%87%BD%E6%95%B0%E9%A2%98%2C%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E6%98%AFx%E5%B1%9E%E4%BA%8ER%E4%B8%94x%E2%89%A00%2C%E5%AF%B9%E5%AE%9A%E4%B9%89%E5%9F%9F%E5%86%85%E7%9A%84%E4%BB%BB%E6%84%8Fx1%E3%80%81x2%E9%83%BD%E6%9C%89f%28x1%C2%B7x2%29%3Df%28x1%29%2Bf%28x2%29%E4%B8%94%E5%BD%93x%EF%BC%9E1%E6%97%B6f%28x%29%EF%BC%9E0%2Cf%282%29%3D1%EF%BC%881%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9Af%28x%29%E6%98%AF%E5%81%B6%E5%87%BD%E6%95%B0%EF%BC%882%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9Af%28x%29%E5%9C%A8%EF%BC%880%2C%E6%AD%A3%E6%97%A0%E7%A9%B7%EF%BC%89%E4%B8%8A%E6%98%AF%E5%A2%9E%E5%87%BD%E6%95%B0%EF%BC%883%EF%BC%89%E8%A7%A3)
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