已知函数f（x）=x的平方+ax+b,且集合A=｛x x=f(x)｝B={x x=f(f(x))}.求证1.A属于B2.A={-1,3}时,用列举法表示B

题目

已知函数f（x）=x的平方+ax+b,且集合A=｛x x=f(x)｝B={x x=f(f(x))}.求证1.A属于B2.A={-1,3}时,用列举法表示B

答案

f（x）=x^2+ax+bA=｛x| x=f(x)｝,B={x| x=f(f(x))}for all x ∈ A=> x = f(x)=> f(x) = f(f(x))=> x = f(f(x)) ( x= f(x))=> x ∈ B=> A is subset of BA={-1,3}x= x^+ax+bx^2+(a-1)x+b=0sum of roots -(a-1) = 2a =...