设f(x)=x方+bx+c.集合A={x|f(x)=x}.B={x|f(x-1)=x+1}若A=2,求集合B.
问题描述：
设f(x)=x方+bx+c.集合A={x|f(x)=x}.B={x|f(x-1)=x+1}若A=2,求集合B.
答
f(x)=x^2+bx+c
f(x)=x
=>x^2+(b-1)x+c = 0
A={2}
=> 4+2(b-1)+c =0
c = -2-2b ---(1)
=>△ =0
f(x)= x^2-3x+4
for B,f(x-1)=x+1
=> (x-1)^2 -3(x-1)+4 = x+1
x=3
=> B ={3}