函数f(x)定义在(-∞,0)∪(0,+∞)上,对定义域中存在x1,x2,使x=x1-x2,f(x1)≠f(x2)且满足以下三个条件①若x1,x2∈(-∞,0)∪(0,+∞),f(x1)≠f(x2)或0<|x1-x2|<a,则f(x1-x2)=[f(x1)*f(x2)+1]/[f(x2)-f(x1)]②f(a)=1(a是一个正
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![函数f(x)定义在(-∞,0)∪(0,+∞)上,对定义域中存在x1,x2,使x=x1-x2,f(x1)≠f(x2)且满足以下三个条件①若x1,x2∈(-∞,0)∪(0,+∞),f(x1)≠f(x2)或0<|x1-x2|<a,则f(x1-x2)=[f(x1)*f(x2)+1]/[f(x2)-f(x1)]②f(a)=1(a是一个正](/uploads/image/z/5411413-37-3.jpg?t=%E5%87%BD%E6%95%B0f%28x%29%E5%AE%9A%E4%B9%89%E5%9C%A8%28-%E2%88%9E%2C0%29%E2%88%AA%280%2C%2B%E2%88%9E%29%E4%B8%8A%2C%E5%AF%B9%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%AD%E5%AD%98%E5%9C%A8x1%2Cx2%2C%E4%BD%BFx%3Dx1-x2%2Cf%28x1%29%E2%89%A0f%28x2%29%E4%B8%94%E6%BB%A1%E8%B6%B3%E4%BB%A5%E4%B8%8B%E4%B8%89%E4%B8%AA%E6%9D%A1%E4%BB%B6%E2%91%A0%E8%8B%A5x1%2Cx2%E2%88%88%28-%E2%88%9E%2C0%29%E2%88%AA%280%2C%2B%E2%88%9E%29%2Cf%28x1%29%E2%89%A0f%28x2%29%E6%88%960%EF%BC%9C%7Cx1-x2%7C%EF%BC%9Ca%2C%E5%88%99f%28x1-x2%29%3D%5Bf%28x1%29%2Af%28x2%29%2B1%5D%2F%5Bf%28x2%29-f%28x1%29%5D%E2%91%A1f%28a%29%3D1%28a%E6%98%AF%E4%B8%80%E4%B8%AA%E6%AD%A3)
函数f(x)定义在(-∞,0)∪(0,+∞)上,对定义域中存在x1,x2,使x=x1-x2,f(x1)≠f(x2)且满足以下三个条件①若x1,x2∈(-∞,0)∪(0,+∞),f(x1)≠f(x2)或0<|x1-x2|<a,则f(x1-x2)=[f(x1)*f(x2)+1]/[f(x2)-f(x1)]②f(a)=1(a是一个正
函数f(x)定义在(-∞,0)∪(0,+∞)上,对定义域中存在x1,x2,使x=x1-x2,f(x1)≠f(x2)且满足以下三个条件
①若x1,x2∈(-∞,0)∪(0,+∞),f(x1)≠f(x2)或0<|x1-x2|<a,则f(x1-x2)=[f(x1)*f(x2)+1]/[f(x2)-f(x1)]
②f(a)=1(a是一个正的常数)
③0<x<2a时,f(x)>0
求证f(x)是奇函数,f(x)在(0,4a)内是减函数
函数f(x)定义在(-∞,0)∪(0,+∞)上,对定义域中存在x1,x2,使x=x1-x2,f(x1)≠f(x2)且满足以下三个条件①若x1,x2∈(-∞,0)∪(0,+∞),f(x1)≠f(x2)或0<|x1-x2|<a,则f(x1-x2)=[f(x1)*f(x2)+1]/[f(x2)-f(x1)]②f(a)=1(a是一个正
F(X+1)在(-∞,0)是减函数,且图像过点(1,0),且为偶函数
故F(X+1)在(0,+∞)是增函数,且图像过点(-1,0).
由此可以画出F(X+1)的示意图(在(-∞,0)是减函数,过点(-1,0).在(0,+∞)是增函数,过点(1,0))
F(X)的图像即是F(X+1)的图像右移1,故F(X)在(-∞,1)是减函数,且过(0,0),在(1,+∞)是增函数,过点(2,0)
故当X2时,F(X)>0;当0