Question

设f(x)是R上的函数,且满足f(0)=1,并且对任意实数都有 f(x-y)=f(x)-y(2x-y+1),求函数f(x

Answer 1

f(0)=1

把x=y代入则f（x-y）=f(x)-y(2x-y+1),

f(0)=f(x)-2x^2+x^2-x=1

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