Question

已知2f(x-1)-f(1-x)=2x^2-1 求f(x)的解析式

Answer 1

令a=x-1,则1-x=-a

2f(a)-f(-a)=2a^2+4a+1 (1)

则a=-a

2f(-a)-f(a)=2a^2-4a+1 (2)

(1)×2+(2)

4f(a)-f(a)=4a^2+8a+2+2a^2-4a+1 =6a^2+4a+3

f(a)=2a^2+4/3a+1

f(x)=2x^2+4/3x+1