已知f（(1-x)/(1+x)）=(1-x^2)/(1+x^2),则f(x)的解析式可取为（ ）A.x/(1+x^2) B.-2x/(1+x^2) C.2x/(1+x^2) D.-x/(1+x^2)
热心网友
应该选择C.2x/(1+x^2)令u=(1-x)/(1+x) == x=(1-u)/(1+u)f(u)={1-[(1-u)/(1+u)]^2}/{1+[(1-u)/(1+u)]^2}=[(1+u)^2-(1-u)^2]/[(1+u)^2+(1-u)^2]=[4u]/[2+2u^2]=(2u)/(1+u^2)即f(x)=(2x)/(1+x^2)
热心网友
3.1415926