Question

已知函数f（x）=1+x^2除以1-x^2 求 f(1除以x)=-f(x)

Answer 1

已知：f(x)=(1+x^2)/(1-x^2)

所以：f(1/x)=(1+1/x^2)/(1-1/x^2)=[(x^2+1)/x^2]/[(x^2-1)/x^2]=(x^2+1)/(x^2-1)=-[(1+x^2)/(1-x^2)]=-f(x)得证.