1.f[(1-x)/(1+x)]=1-x^2/1+x^2,求f(x)备注:x^2是x的平方2.已知2f(x)+f(-x)=3x+2,求f(x)3.已知f(x)+2f(1/x)=2x+1,求f(x)
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1.f[(1-x)/(1+x)]=1-x^2/1+x^2,求f(x)备注:x^2是x的平方2.已知2f(x)+f(-x)=3x+2,求f(x)3.已知f(x)+2f(1/x)=2x+1,求f(x)
1.f[(1-x)/(1+x)]=1-x^2/1+x^2,求f(x)
备注:x^2是x的平方
2.已知2f(x)+f(-x)=3x+2,求f(x)
3.已知f(x)+2f(1/x)=2x+1,求f(x)
1.f[(1-x)/(1+x)]=1-x^2/1+x^2,求f(x)备注:x^2是x的平方2.已知2f(x)+f(-x)=3x+2,求f(x)3.已知f(x)+2f(1/x)=2x+1,求f(x)
中括号内的内容不是过程.
1.设(1-x)/(1+x)=t,则X=1-t/1=t t≠-1.[x≠-1这是定义域]
[将X=1-t/1+t带入f(x)后,将x全换成f(t)的形式.再将t全换成x,得到f(x)的形式]
带入原式得:f(x)=1-(1-x/1+x)^2/1+(1-x/1+x)^2,x≠-1.
2.由题意得,f(-x)=3x+2-2f(x)①,故f(x)=-3x+2-2f(-x)②
将①带入②式整理得:f(x)=3x+2/3
3题同2题一样.
3.由题意得,f(1/x)=[2x+1-f(x)]/2①,故f(x)=2/x+1-f(1/x)②
将①带入②式整理得:f(x)=4/x-2x+1.
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