函数f(x)对一切实数x,y都有f(x+y)-f(y)=(x+2y+1)x成立,且f(1)=0,求f(0)及f(x)
问题描述:
函数f(x)对一切实数x,y都有f(x+y)-f(y)=(x+2y+1)x成立,且f(1)=0,求f(0)及f(x)
答
令x=1,y=0,则f(x+y)-f(y) = f(1) - f(0) = 2
故f(0) = -2
再令y=0,
f(x)-f(0) = (x+1)x
因此f(x) = x(x+1)-2