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JEE Main202120 Jul 2021Morning ShiftMathematicsFunctionsActual

Let x denote the greatest integer ≤ x , where x ∈ R . If the domain of the real valued function f x = x - 2 x - 3 is - ∞ , a ∪ b , c ∪ 4 , ∞ , a < b < c , then the value of a + b + c is:

Options

  1. A8
  2. B1
  3. C- 2
  4. D- 3

Correct answer

C. - 2

Step-by-step solution

We have, f x = x - 2 x - 3 For domain, x - 2 x - 3 ≥ 0 Case I : When | [ x ] | - 2 ≥ 0 and x - 3 > 0 , then ∴   x ∈ - ∞ , - 3 ∪ 4 , ∞         . . . 1 Case II : When x - 2 ≤ 0 and x - 3 < 0 , then ∴   x ∈ - 2 , 3       . . . 2 So, from 1 and 2 , we get Domain of function is - ∞ , - 3 ∪ - 2 , 3 ∪ 4 , ∞ ∴   a + b + c = - 3 + - 2 + 3 = - 2 ∵   a < b < c

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