Question

【考查导数概念】设函数f(x)在整个实数域上有定义,对于任意x,y,f(x)满足：f(x+y)-f(x)=[f(x)-1

Answer 1

f(x+y)-f(x)=[f(x)-1]y+h(y)

令x=0

则 f(y)-f(0)=[f(0)-1]y+h(y)

f(y)-2=y+h(y)

f'(y)=1

f(y)=y+c

令y=0,得f(0)=c=2

则f(y)=y+2

即 f(1)=1+2=3