​ Let [x] denote the greatest integer ≤ x, where x ∈ R. If the domain of the real valued function f(x) = √|[x]|-2/|[x]|-3

Question

Let [x] denote the greatest integer ≤ x, where x ∈ R. If the domain of the real valued function

f(x) = \(\sqrt{\frac{|[x]|-2}{|[x]|-3}}\)

√|[x]|-2/|[x]|-3

is (-∞, a) ∪ [b, c) ∪ [4, ∞), a<b<c, then the value of a + b + c is:

(1) 8

(2)1

(3) -2

(4) –3

Answer 1

Answer is: (3) -2

For domain,

So, from (1) and (2) we get

Domain of function

Comments

Case 2 kaise aaya?

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For Case II: If |[x]| -2 ≤ 0 & |[x]| - 3 < 0
Then {|[x]| - 2}/{|[x]| - 3} ≥ 0

If |[x]| - 2 ≤ 0 ⇒ |[x]| ≤ 2
⇒ -2 ≤ [x] ≤ 2
⇒ x ∈ [-2, 3)

And |[x]| - 3 < 0 ⇒ |[x]| < 3
⇒ -3 < [x] < 3
⇒ x ∈ [-2, 3)
∴ x ∈ [-2, 3)

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Kyunki jb dono factors -ve honge TB bhi resultant
+Ve hoga.