Question

设函数f:R - R满足f(0)=1,且对任意x,y属于R,均有f(xy+1)=f(x)f(y)-f(y)-x+2则有f

Answer 1

令 x = y = 0得：

f(1)

= f(0)×f(0) - f(0) - 0 + 2

= 1×1 - 1 - 0 + 2

= 2

令 y = 0得：

f(1) = f(x)×f(0) - f(0) -x + 2

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

f(x) = x + 1