f(x)=arcsin 2x/(1+x) + √(1-2x-3x^2)的定义域是?

来源：学生作业帮助网编辑：作业帮时间：2024/04/24 08:24:45

f(x)=arcsin 2x/(1+x) + √(1-2x-3x^2)
case 1:
1-2x-3x^2 > 0
3x^2+2x-1<0
(3x-1)(x+1)<0
-1and
case 2:
1+x 不等于0
x不等于-1
and
case 3:
-1<=2x <= 1
-1/2 <=x <=1/2
定义域
case 1 and case 2 and case 3
-1ie -1/2 <=x < 1/3

1
-1<=2x/(1+x)<=1
1+x>0 2x<=1+x , 1>=x>-1
2x>=-1-x x>=-1/3
2
1-2x-3x^2>=0
3x^2+2x-1<=0
(3x-1)(x+1)<=0
-1<=x<=1/3
3
-1/3<=x<=1/3

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