函数F(X)与数列结合的题目求解已知f(x)在(-1,1)上有定义,f(1/2)=-1,且满足x,y属于(-1,1)有f(x)+f(y)=f((x+y)/(1+xy))(1)证明f(x)在(-1,1)上为奇函数(2)对数列x1=1/2,x(n+1)=2x(n)/(1+x(n)^2),求f(xn)(3)求证1/f
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![函数F(X)与数列结合的题目求解已知f(x)在(-1,1)上有定义,f(1/2)=-1,且满足x,y属于(-1,1)有f(x)+f(y)=f((x+y)/(1+xy))(1)证明f(x)在(-1,1)上为奇函数(2)对数列x1=1/2,x(n+1)=2x(n)/(1+x(n)^2),求f(xn)(3)求证1/f](/uploads/image/z/693452-20-2.jpg?t=%E5%87%BD%E6%95%B0F%28X%29%E4%B8%8E%E6%95%B0%E5%88%97%E7%BB%93%E5%90%88%E7%9A%84%E9%A2%98%E7%9B%AE%E6%B1%82%E8%A7%A3%E5%B7%B2%E7%9F%A5f%28x%29%E5%9C%A8%EF%BC%88-1%2C1%EF%BC%89%E4%B8%8A%E6%9C%89%E5%AE%9A%E4%B9%89%2Cf%281%2F2%29%3D-1%2C%E4%B8%94%E6%BB%A1%E8%B6%B3x%2Cy%E5%B1%9E%E4%BA%8E%EF%BC%88-1%2C1%EF%BC%89%E6%9C%89f%28x%29%2Bf%28y%29%3Df%28%28x%2By%29%2F%281%2Bxy%29%29%281%29%E8%AF%81%E6%98%8Ef%28x%29%E5%9C%A8%EF%BC%88-1%2C1%EF%BC%89%E4%B8%8A%E4%B8%BA%E5%A5%87%E5%87%BD%E6%95%B0%282%29%E5%AF%B9%E6%95%B0%E5%88%97x1%3D1%2F2%2Cx%EF%BC%88n%2B1%EF%BC%89%3D2x%28n%29%2F%281%2Bx%28n%29%5E2%29%2C%E6%B1%82f%28xn%29%283%29%E6%B1%82%E8%AF%811%2Ff)
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