Question

高一数学第十八题，求过程~

Answer 1

(1) 令y=0 得f(x)-f(0)=x(x+1) f(x)=x(x+1)+f(0)
再令x=1 得f(1)=2+f(0)=0

f(0)=-2

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

Answer 2

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