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Find range of the function f(X)=|x-1|+|x-2|+.........|x-100| and discuss about graph of f(X)

Find range of the function f(X)=|x-1|+|x-2|+.........|x-100| and discuss about graph of f(X)

Grade:12th pass

2 Answers

Aditya Gupta
2081 Points
5 years ago
Actually the least value of |x-a1|+|x-a2|+.....+|x-a2n| such that a1, a2,...,a2n are in ascending order is attained at x belonging to [an, an+1]
So least value of above expression is attained at 50.
So it's value at 50 is 2(1+2+...+49)+50
= 2500
So range is [2500, infinty]
Aditya Aditya jha
13 Points
2 years ago
|x-1|&|x-100|is greater than or equal to  99,X belongs to [1,100]
|x-2|&|x-99|is greater than or equal to 97,x belongs to [2,99]
 same for others 
for |x-50| &|x-51|it is greater than or equal to 1,x belongs to [50,51]
Ymin=1+3+5+........99=(50)^2=2500 
so ,
Rf=Y belongs to [2500,infinity)

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