解由f(x)+g(x)=x²+x+1.①
用-x代替x代入①得
f(-x)+g(-x)=（-x）²+（-x）+1
又由f(x)为奇函数,g(x)为偶函数,
即-f（x）+g（x）=x^2-x+1.②
由由①+②得
g（x）=x^2+1
由①-②得
f（x）=x