It is known that the image of f (x) = x (-n 2+2n+3) (n = 2k, k ∈ z) monotonically increases on (0, +∞), and the inequality f (x 2-x) >: f(x+3).

f(x)=x^(-n^2+2n+3)

=x^[(-n+3)(n+ 1)]

N=2k is an even number.

(-n+3)(n+ 1) is an odd number.

f(-x)=(-x)^(-n^2+2n+3)=-x^(-n^2+2n+3)=-f(x)

F(x) is odd function.

F(x) monotonically increases on r.

x^2-x>； x+3

x^2-2x-3>； 0

(x-3)(x+ 1)>0

x & lt- 1x & gt； three