已知f(x)=x[1\(-n^2+2n+3)](n属于Z)的图像在[0,正无穷)上单调递增,解不等式f(x^2-x)>f(x+3)
问题描述:
已知f(x)=x[1\(-n^2+2n+3)](n属于Z)的图像在[0,正无穷)上单调递增,解不等式f(x^2-x)>f(x+3)
答
已知f(x)=x[1\(-n^2+2n+3)](n属于Z)的图像在[0,正无穷)上单调递增1\(-n^2+2n+3)>0f(x^2-x)>f(x+3) (x^2-x)[1\(-n^2+2n+3)]>(x+3)[1\(-n^2+2n+3)] x^2-x>x+3x^2-2x-3>0(x-3)(x+1)>0解得x3