f(x1-x2)=f(x1)*f(x2)+1/f(x2)-f(x1)求证f(x)为奇函数
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f(x1-x2) = f(x1)*f(x2) + 1 / [ f(x2)-f(x1) ]

f[-(x1-x2)] = f(x2-x1)

= f(x2)*f(x1) + 1 / [ f(x1)-f(x2) ]

= - {- f(x2)*f(x1) - 1 / [ f(x1)-f(x2) ] }

= - { f(x1)*f(x2) + 1 / [ f(x2)-f(x1) ] }

= - f(x1-x2)

f[-(x1-x2)] = - f(x1-x2)

∴f(-x) = -f(x)

∴奇函数

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