已知y=f(x)(x∈R)与y=g(x)(x∈A)互为反函数,且对任意的实数a,b有f(a+b)=f(a)f(b).求证:对任意的实数m,n∈A,有mn∈A且g(mn)=g(m)+g(n).越快越好.
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![已知y=f(x)(x∈R)与y=g(x)(x∈A)互为反函数,且对任意的实数a,b有f(a+b)=f(a)f(b).求证:对任意的实数m,n∈A,有mn∈A且g(mn)=g(m)+g(n).越快越好.](/uploads/image/z/6229325-29-5.jpg?t=%E5%B7%B2%E7%9F%A5y%3Df%28x%29%28x%E2%88%88R%29%E4%B8%8Ey%3Dg%28x%29%28x%E2%88%88A%29%E4%BA%92%E4%B8%BA%E5%8F%8D%E5%87%BD%E6%95%B0%2C%E4%B8%94%E5%AF%B9%E4%BB%BB%E6%84%8F%E7%9A%84%E5%AE%9E%E6%95%B0a%2Cb%E6%9C%89f%28a%2Bb%29%3Df%28a%29f%28b%29.%E6%B1%82%E8%AF%81%EF%BC%9A%E5%AF%B9%E4%BB%BB%E6%84%8F%E7%9A%84%E5%AE%9E%E6%95%B0m%2Cn%E2%88%88A%2C%E6%9C%89mn%E2%88%88A%E4%B8%94g%28mn%29%3Dg%28m%29%2Bg%28n%29.%E8%B6%8A%E5%BF%AB%E8%B6%8A%E5%A5%BD.)
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