Question

若f(x-1)+2f(1-x)=2x,求f(x)

Answer 1

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

令a=x-1,则x=a+1,1-x=-a

所以f(a)+2f(-a)=2a+2

即f(x)+2f(-x)=2x+2 (1)

令b=-x,x=-b

f(-b)+2f(b)=-2b+2

所以f(-x)+2f(x)=-2x+2 (2)

(2)×2-(1)

3f(x)=-6x+2

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