已知函数f(x)的定义域为R,满足f(-x)=1/f(x)>0,且g(x)=f(x)+c(c为常数)在区间[a,b]上是减函数.判断并证明g(x)在区间[-b,-a]上的单调性.
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![已知函数f(x)的定义域为R,满足f(-x)=1/f(x)>0,且g(x)=f(x)+c(c为常数)在区间[a,b]上是减函数.判断并证明g(x)在区间[-b,-a]上的单调性.](/uploads/image/z/2520847-55-7.jpg?t=%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%E4%B8%BAR%2C%E6%BB%A1%E8%B6%B3f%28-x%29%3D1%2Ff%28x%29%3E0%2C%E4%B8%94g%28x%29%3Df%28x%29%2Bc%28c%E4%B8%BA%E5%B8%B8%E6%95%B0%29%E5%9C%A8%E5%8C%BA%E9%97%B4%5Ba%2Cb%5D%E4%B8%8A%E6%98%AF%E5%87%8F%E5%87%BD%E6%95%B0.%E5%88%A4%E6%96%AD%E5%B9%B6%E8%AF%81%E6%98%8Eg%28x%29%E5%9C%A8%E5%8C%BA%E9%97%B4%5B-b%2C-a%5D%E4%B8%8A%E7%9A%84%E5%8D%95%E8%B0%83%E6%80%A7.)
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