Question

已知 f [ (1-x)/(1+x) ] = (1-x^2)/(1+x^2) .则 f(x)的解析式为?

Answer 1

f((1-x)/(1+x))=(1-x^2)/(1+x^2)

令t=(1-x)/(1+x)

f(t)=(1-x^2)/(1+x^2)

t(1+x)=1-x

tx+x=1-t

x(t+1)=1-t

x=(1-t)/(1+t)

f(t)=2t/(1+t^2)

f(x)=2x/(1+x^2)