Question

2f（x-1）+f（3-x）＝x2 求f（x）表达式

Answer 1

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

令x-1=t

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

令3-x=t

2f(2-t)+f(t)=（3-t）^2 (2)

(1)*2-(2)得

3f(t)=2(1+t)^2-(3-t)^2

3f(t)=2+4t+2t^2-9+6t-t^2

3f(t)=t^2+10t-7

f(t)=1/3t^2+10/3t-7/3

则有

f(x)=1/3x^2+10/3x-7/3