已知函数f(x)=x^2/(1+x^2),试求f(1)+f(2)+f(1/2)+f(3)+f(1/3)+f(4)+f(1/4)的值!!!!!!!!

因为f(x)+f(1/x) =x^2/(1+x^2)+(1/x^2)/[1+(1/x^2)] =x^2/(1+x^2)+1/(1+x^2) =(1+x^2)/(1+x^2) =1 所以 f(2)+f(1/2)=1 f(3)+f(1/3)=1 f(4)+f(1/4)=1 原式=f(1)+[f(2)+f(1/2)]+[f(3)+f(1/3)]+[f(4)+f(1/4)] =f(