Question

函数f(x)=（1+x平方）分之x平方,x∈R（1）求f(x)+f(1/x) 和求f(1)+f(2)+f(3)+f(4)

Answer 1

(1)

f(x)=x²/(1+x²)

=1-1/(1+x²)

f(1/x)= 1-1/(1+1/x²)=1-1/[(1+x²)/x²]=1-x²/(1+x²)=1-f(x)

所以f(x)+f(1/x)= 1

f(1)+f(2)+f(3)+f(4)+f(1/2)+f(1/3)+f(1/4)

= f(1)+[f(2)+f(1/2)]+[f(3)+f(1/3)]+[f(4)+f(1/4)]

=1/(1+1)+1+1+1

=7/2