Let -x- denote the greatest integer - x- where x - If the domain of the real valued function fx-x-2-x-3 is -a-b-c-4- a-b-c- then the value of a-b-c is

|[x]| 2|[x]| 3≥ 0⇒ |[x]|≤ 2 or |[x]| gt;3 ⇒ 2≤[x]≤ 2 or [x] lt; 3 or [x] gt;3 ⇒ 2 ≤ x lt; 3 or x lt; 3 or x ≥ 4 ⇒ x∈ ( ∞, 3)∪[ 2,3)∪[4,∞) a = 3, ...

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Standard XII

Mathematics

Greatest Integer Function

Let [x] denot...

Question

Let $[x]$ denote the greatest integer $\leq x$ , where $x \in R$ . If the domain of the real valued function $f (x) = \sqrt{\frac{| [x] | - 2}{| [x] | - 3}}$ is $(- \infty, a) \cup [b, c) \cup [4, \infty),$ $a < b < c,$ then the value of $a + b + c$ is

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Solution

The correct option is B $- 2$
$\frac{| [x] | - 2}{| [x] | - 3} \geq 0 \Rightarrow | [x] | \leq 2$ or $| [x] | > 3$
$\Rightarrow - 2 \leq [x] \leq 2$ or $[x] < - 3$ or $[x] > 3$
$\Rightarrow - 2 \leq x < 3$ or $x < - 3$ or $x \geq 4$
$\Rightarrow x \in (- \infty, - 3) \cup [- 2, 3) \cup [4, \infty)$
$a = - 3, b = - 2, c = 3$

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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

The correct option is B −2|[x]|−2|[x]|−3≥0⇒|[x]|≤2 or |[x]|>3 ⇒−2≤[x]≤2 or [x]<−3 or [x]>3 ⇒−2≤x<3 or x<−3 or x≥4 ⇒x∈(−∞,−3)∪[−2,3)∪[4,∞) a=−3,b=−2,c=3

Let $[x]$ denote the greatest integer $\leq x$ , where $x \in R$ . If the domain of the real valued function $f (x) = \sqrt{\frac{| [x] | - 2}{| [x] | - 3}}$ is $(- \infty, a) \cup [b, c) \cup [4, \infty),$ $a < b < c,$ then the value of $a + b + c$ is