1若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)大于f(x+3)

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1若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)大于f(x+3)

1若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)大于f(x+3)
1若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)大于f(
x+3)

1若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)大于f(x+3)
依题意,-n^2+2n+3>0,解得 -1<n<3
因为 n∈Z,所以 n=0,1,2
1)当n=0或2时,f(x)=x^(1/3),是奇函数,
所以 f(x)在R上为增函数,不等式f(x^2-x)>f(x+3)等价于 x^2-x>x+3
解得 x<-1或x>3
2)当n=1时,f(x)=x^(1/4),(x≥0)
所以,不等式f(x^2-x)>f(x+3)等价于 x^2-x>x+3 且x^2-x≥0 且 x+3≥0
解得 x>3