偶函数f(x)定义域为R,且在(负无穷,0]上单调递减,求满足f(x^2+2x+3)>f(3x-4x^2-1)的x的集合

问题描述:

偶函数f(x)定义域为R,且在(负无穷,0]上单调递减,求满足f(x^2+2x+3)>f(3x-4x^2-1)的x的集合

|x^2+2x+3|>|3x-4x^2-1|
x^2+2x+3=(x+1)²+2≥0
①x^2+2x+3>3x-4x^2-1
5x²-x+4>0,
x∈R都成立
②x^2+2x+3>-(3x-4x^2-1)
3x²-5x-2