Relations Question 2
Question: The range of the function $ f(x)=| x-1 |+| x-2 |,-1\le x\le 3 $ is
Options:
A) $ [ 1,3 ] $
B) $ [1,5] $
C) $ [ 3,5 ] $
D) none of these
Show Answer
Answer:
Correct Answer: B
Solution:
Clearly, form the graph, the range is $ [1,f(-1)]\equiv [1,5]. $
If $ x<1,f(x)=-(x-1)-(x-2)=-2x+3. $
In this interval, $ f(x) $ is decreasing.
If $ 1\le x<2,f(x)=x-1-(x-2)=1. $
In this interval, $ f(x) $ is constant. If $ 2\le x\le 3. $
$ f(x)=x-1+x-2=2x-3. $
In this interval. $ f(x) $ is increasing.
$ \therefore \max f(x)= $ the greatest among $ f(-1) $ and $ f(3)=5 $ , $ \min f(x)=f(1)=1 $ So, range= [1, 5]
BETA
