IIT JEE 1983 Maths - MCQ Question 18
Algebra
Level
3
If satisfies , then which option is correct?
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or
or
None of the others
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1 solution
f(x) = |x-1| + |x-2| + |x-3|
f(x) = ⎩ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎧ 6 − 3 x 4 − x x 3 x − 6 x ≤ 1 1 ≤ x ≤ 2 2 ≤ x ≤ 3 3 ≤ x r a n g e ( 3 , in f ) r a n g e ( 0 , 2 ) r a n g e ( 2 , 2 ) r a n g e ( 3 , in f )
The only regions which we need to analyze are x<1 and x>3.
By plotting the function we can see that x ≤ 0 and x ≥ 4 are the desired regions.