Question

已知若函数y=f(x)的定义域是[-1,1],求下列函数的定义域:y=f(x-1/2)+f(x+1/2)

Answer 1

因为函数y=f(x)的定义域是[-1,1],
所以-1=<x<=1
-3/2=<x-1/2<=1/2
-1/2=<x+1/2<=3/2
所以-1/2=<x<=1/2
所以y=f(x-1/2)+f(x+1/2)定义域是[-1/2,1/2]

Answer 2

由题意可知，-1≤x-1/2≤1,-1≤x 1/2≤1,解得-1/2≤x≤1/2，即为所求。