已知函数FX=1+X平方分之X平方,当X不等于0时,证明FX+F X分之1=1 求F1+F2+F3+F4+F2分之1+F

f(x)=x^2/(1+x^2)
f(x)+f(1/x)=x^2/(1+x^2)+(1/x^2)/[1+(1/x^2)]
=x^2/(1+x^2)+1/(x^2+1)=(1+x^2)/(1+x^2)=1
f(1)+(2)+f(3)+f(4)+f(1/2)+f(1/3)+f(1/4)
=f(1)+(2)+f(1/2)+f(3)+f(1/3)+f(4)+f(1/4)
=f(1)+[(2)+f(1/2)]+[f(3)+f(1/3)]+[f(4)+f(1/4)]
=1/2+1+1+1=3+1/2=3.5=7/2