Question

已知2f(x)-f(-x)=x^2-x+1,求f(x),

Answer 1

2f(x)-f(-x)=x^2-x+1 (1)

x取-x

2f(-x)-f(x)=x^2+x+1 (2)

(1)+(2)

f(x)+f(-x)=2x^2+2 (3)

(1)+(3)

3f(x)=3x^2-x+3

f(x)=x^2-x/3+1