Question

若函数f(x)的定义域是【-2，2】，求函数f(x2-x-4)的定义域

步骤具体些。。谢谢

Answer 1

f(x)的定义域是【-2，2】
则f(x2-x-4)中-2<=x²-x-4<=2

x²-x-4>=-2
x²-x-2=(x-2)(x+1)>=0
x<=-1,x>=2

x²-x-4<=2
x²-x-6=(x-3)(x+2)<=0
-2<=x<=3
所以-2<=x<=-1,2<=x<=3
所以定义域是[-2,-1]∪[2,3]

Answer 2

-2<=x^2-x-4<=2
-2<=x^2-x+1/4-17/4<=2
9/4<=x^2-x+1/4<=25/4
9/4<=(x-1/2)^2<=25/4
当
(x-1/2)^2>=9/4时
x-1/2>=3/2或 x-1/2<=-3/2
x>=2或x<=-1
当(x-1/2)^2<=25/4时
-5/2<=x-1/2<=5/2
-2<=x<=3
结合起来就是
-2<=x<=-1或 2<=x<=3

Answer 3

f(x)的定义域是【-2，2】，即-2<=x<=2
令-2<=x^2-x-4<=2
x^2-x-4>=-2
x^2-x-2>=0
(x-2)(x+1)>=0
x>=2,x<=-1......(1)
x^2-x-4<=2
x^2-x-6<=0
(x-3)(x+2)<=0
-2<=x<=3.....(2)
取（1）（2）的交集得：2<=x<=3或-2<=x<=-1
即函数f(x2-x-4)的定义域[-2，-1]U[2，3]