f(x) = Ix-1I + Ix-2I ,-1<_x<_3

Find the range

range [1,5]

f(x) = |x - 1| + |x - 2|

      = 2x - 3 , x > 2

               1   , 1 < x < 2

        - 2x + 3 , x < 1

Clearly, range of f(x) is [1,5].

 f(x) = |x - 1| + | x-2|

(-1) ---------------------(1)--------------------(2)-------------------(3)

            -X+1-(X-2)              X-1-X+2                   X-1+X-2            

        F(X)=-2X+3                F(X) =1                    F(X)=2X-3       

DECREASING                  CONSTANT            INCREASING

SO MAX = 5                       SO MAX AND            MAX = 6-3 = 3

MIN =1                               MIN BOTH = 1          MIN = 1

CONSIDERING WHOLE DOMAIN WE ARE GETTING MAXIMUM AS 5 AND MINIMUM AS 1...