优质解答
因为f(x)=(1-x^2)/(1+x^2),则
(1) f(-x)=[1-(-x)^2]/[(1+(-x)^2]
=(1-x^2)/(1+x^2)
=f(x)
(2)f(1/x)=[1-(1/x)^2]/[(1+(1/x)^2]
=(1-1/x^2)/(1+1/x^2)
=[(x^2-1)/x^2]/[(x^2+1)/x^2]
=(x^2-1)/(1+x^2)
=-(1-x^2)/(1+x^2)
=-f(x)
因为f(x)=(1-x^2)/(1+x^2),则
(1) f(-x)=[1-(-x)^2]/[(1+(-x)^2]
=(1-x^2)/(1+x^2)
=f(x)
(2)f(1/x)=[1-(1/x)^2]/[(1+(1/x)^2]
=(1-1/x^2)/(1+1/x^2)
=[(x^2-1)/x^2]/[(x^2+1)/x^2]
=(x^2-1)/(1+x^2)
=-(1-x^2)/(1+x^2)
=-f(x)