Question

已知函数f（x）=1/x^2+1,令g（x）=f（1/x）求证f（x）+g（x）=1（x≠0）

Answer 1

打错了?f(x)=1/(x^2+1)

g(x)=f(1/x)=1/[(1/x)^2+1]=1/[(x^2+1)/x^2]=x^2/(x^2+1)

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

得证