Question

已知函数f(x)=x2+ax+b,且集合A={x|x=fx},B={x|x=f[f(x)]},(1)求证A包含于B;(2

Answer 1

(1)

所有 x ∈ A

=> x = f(x)

=>f(x) = f(f(x))

=> x = f(f(x)) ( x= f(x))

=> x ∈ B

=> A 是 B 的子集

(2)

A={-1,3}=> B = {-1,3}