Question

1.已知函数f(x)的定义域为[1,3],求f(2x-3)的定义域 2.设函数f(2x+1)的定义域[-3，5],求f(x)的定义域

Answer 1

1、
1<=2x-3<=3
4<=2x<=6
2<=x<=3
所以f(2x-3)的定义域是[2,3]

2、
f(2x+1)的定义域[-3，5]
即-3<=x<=5
-6<=2x<=10
-5<=2x+1<=11
所以f(x)定义域是[-5,11]

Answer 2

1. 1≤2x-3≤3
4≤2x≤6
2 ≤x≤3
f(2x-3)的定义域[2,3]
2. -3 ≤2x1 ≤5
-4 ≤2x ≤4
-2 ≤x ≤2
f(x)的定义域[-2,2]