If fx-3-x-x-2- then complete set of domain of f is

F(x)=√(3|x| x 2) is defined when nbsp;3|x| x 2≥0 Case 1: When x lt;0 3x x 2≥0 ⇒ x≤ 12 ⇒ x∈( ∞, 12] Case 2: When x≥0 3x x 2≥0 ⇒ x≥1 ⇒ x∈ [1,∞) Hence, dom ...

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Byju's Answer

Standard XII

Mathematics

Domain

If fx=√3|x|-x...

Question

If $f (x) = \sqrt{3 | x | - x - 2},$ then complete set of domain of $f$ is

(- \infty, - \frac{1}{2}] \cup [2, \infty)

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(- \infty, 1]

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(- \infty, - \frac{1}{2}] \cup [1, \infty)

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[- \frac{1}{2}, \infty)

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Solution

The correct option is C $(- \infty, - \frac{1}{2}] \cup [1, \infty)$
$f (x) = \sqrt{3 | x | - x - 2}$ is defined when $3 | x | - x - 2 \geq 0$

Case $1 :$ When $x < 0$
$- 3 x - x - 2 \geq 0 \Rightarrow x \leq - \frac{1}{2}$
$\Rightarrow x \in (- \infty, - \frac{1}{2}]$

Case $2 :$ When $x \geq 0$
$3 x - x - 2 \geq 0 \Rightarrow x \geq 1$
$\Rightarrow x \in [1, \infty)$

Hence, domain of $f$ is $(- \infty, - \frac{1}{2}] \cup [1, \infty)$

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If f(x)=√3|x|−x−2, then complete set of domain of f is

The correct option is C (−∞,−12]∪[1,∞)f(x)=√3|x|−x−2 is defined when 3|x|−x−2≥0 Case 1: When x<0 −3x−x−2≥0⇒x≤−12 ⇒x∈(−∞,−12] Case 2: When x≥0 3x−x−2≥0⇒x≥1 ⇒x∈[1,∞) Hence, domain of f is (−∞,−12]∪[1,∞)

If $f (x) = \sqrt{3 | x | - x - 2},$ then complete set of domain of $f$ is