Question

已知f(1加x分之1减x)=1加x平方分之1减x平方,则f(x)的解析式可取为?

Answer 1

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

令y=(1-x)/(1+x)

=>x=(1-y)/(1+y)

=>f(y)=(1-(1-y)^2/(1+y)^2)/(1+(1-y)^2/(1+y)^2)

=2y/(1+y^2)

将y替换成x

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