Question

已知函数fx的定义域是[-2,4]，求函数gx=fx+f-x的定义域

Answer 1

根据题意:x要满足f(x),f(-x)都有定义
所以
-2<=x<=4
-2<=-x<=4即-4<=x<=2
上面两式取交,得-2<=x<=2
所以g(x)的定义域是[-2,2]

Answer 2

-4<=x<=3
-4<=-x<=3
-3<=x<=4
取交集
-3<=x<=3
∴f(x)定义域是[-3,3]
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