Question

急！！数学题:已知函数f(x)=x-1的绝对值+x-2的绝对值

(1)若f(x)>=m恒成立，求实数m的取值范围！(2)f(x)<=2,求实数x的取值范围

Answer 1

x<=1时,|x-1|＝1-x,|x-2|＝2-x,f(x)＝3-2x>=3-2=1
1<x<2时,|x-1|＝x-1,|x-2|＝2-x,f(x)=1
x>＝2时,|x-1|＝x-1,|x-2|＝x-2,f(x)=2x-3>=4-3=1
所以m<＝1

x<=1时,3-2x<=2,1=>x>=1/2
x>=2时,2x-3<=2,2<=x<=5/2

Answer 2

(1)m<=1
(2)0.5<=x<=2.5
f(x)实际上就是x点到1和到2的距离之和

Answer 3

（1）m<=1
(2)0.5<=x<=2.5

Answer 4

m<=1
0.5=<x<=2.5