已知函数f(x+1)的定义域为[-2,3],求f(2x^2-2)的定义域

RT
2025-01-08 17:22:00
推荐回答(1个)
回答1:

函数f(x+1)的定义域为[-2,3],
-2<=x<=3
-1<=x+1<=4
即函数f(x)的定义域是[-1,4]
-1<=2x^2-2<=4
1/2<=x^2<=3
x^2>=1/2得:x>=根号2/2或x<=-根号2/2
x^2<=3得-根号3<=X<=根号3

取交集得:根号2/2<=X<=根号3或-根号3<=X<=-根号2/2.
以上即为定义域