已知函数fx=x²+x+1/x²+1若f（a）=2/3,则f（-a）=

已知函数fx=x²+x+1/x²+1若f（a）=2/3,则f（-a）=
已知函数fx=x²+x+1/x²+1若f（a）=2/3,则f（-a）=

已知函数fx=x²+x+1/x²+1若f（a）=2/3,则f（-a）=
f(x) = (x²+x+1) / (x²+1)
= [(x²+1)+x] / (x²+1)
= 1 + x/(x²+1)
= 1 + 1/(x+1/x)
f(a)=1+1/(a+1/a) = 2/3
1/(a+1/a) = -1/3
f(-a) = 1 + 1/[-a+1/(-a)] = 1 - 1/(a+1/a) = 1-(-1/3) = 4/3

因为函数是偶函数，所以f(-a)=f(a)=2/3