高一求函数最值题f(x)=(x-1)/(x 1),x属于[1,3]_数学解答

高一求函数最值题
f(x)=(x-1)/(x 1),x属于[1,3]

人气：127 ℃　时间：2020-06-03 16:31:06

解答

f(x)=(x-1)/(x+ 1)=(x+1-2)/(x+1)=1-2/(x+1),
由于:2<=x+1<=4,故1/4<=1/(x+1)<=1/2
-1<=-2/(x+1)<=-1/2
0<=1-2/(x+1)<=1/2
所以,0<=f(x)<=1/2,即值域是[0,1/2]