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【简答题】
已知定义域为R的函数y=f(x)和y=g(x),它们分别满足条件:对任意a,b∈R,f(a+b)=f(a)+f(b);对任意a,b∈R,g(a+b)=g(a)?g(b),且对任意x>0,g(x)>1. (1)求f(0)、g(0)的值; (2)证明函数y=f(x)是奇函数; (3)证明x<0时,0<g(x)<1,且函数y=g(x)在R上是增函数; (4)试各举出一个符合函数y=f(x)和y=g(x)的实例.
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