函数f(x)=x2+mx+n,A{x|f(x)=x},B{x|f(x-1)>x+5},若A={3},求集合B?

A={3}
f(x) =x
x^2+mx+n =x
x^2+(m-1)x + n =0
consider
(x-3)^2 =0
x^2-6x+9 =0
compare the coef. of x and constant, we get
m-1 = -6 and n = 9
m = -5 and n = 9
=> f(x) = x^2-5x+9
for B
f(x-1) > x+5
(x-1)^2-5(x-1)+9 > x+5
x^2-8x+10 > 0
x > 4+√6 or x < 4-√6
B = {x | x > 4+√6 or x < 4-√6 }