已知函数fx=x²+x+1/x²+1若f(a)=2/3,则f(-a)=
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![已知函数fx=x²+x+1/x²+1若f(a)=2/3,则f(-a)=](/uploads/image/z/13298327-71-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0fx%3Dx%26%23178%3B%2Bx%2B1%2Fx%26%23178%3B%2B1%E8%8B%A5f%EF%BC%88a%EF%BC%89%3D2%2F3%2C%E5%88%99f%EF%BC%88-a%EF%BC%89%3D)
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