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CBSE Class 12-science Answered

Find the range of the function f(x)= |x-1|+|x-2| where x lies in [-1,3]
Asked by Anupriya | 22 May, 2013, 11:53: PM
answered-by-expert Expert Answer
 f(x)= |x-1|+|x-2| 
f(x) = -2x+3 (x<=1) ; 1 (1<x<=2) ; 2x-3 (x>2)
 
On plotting the 3 equations in a x-y graph for specified range of x, we will find that the function is a V -shaped function, with decreasing straight line for x<1 and then constant for x between 1 and 2 and then it is an increasing function. 
 
So, for x between -1 and 3, f(x) will vary from [1,5] 
 
Hence, range of the function is [1,5] when x lies in [-1,3]
 
hence for (-1<=x<=3), 
Answered by | 23 May, 2013, 02:40: AM

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