Values of x for which -4-x2 is defined- lies in the intervalA- -4-4-B- -4-4-C- -4-4D- -4-4

The correct option is A [ 4,4] nbsp;√(4 √(x^2))=√(4 |x|) √(4 |x|) is defined when 4 |x|≥ 0 When x ≥ 0 4 x ≥ 0 ⇒ x≤ 4 ⇒ x∈ [0,4] When x 0 4+x ≥ 0 ⇒ x ≥ 4 ⇒ ...

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Standard XII

Mathematics

Absolute Value Function

Values of x f...

Question

Values of $x$ for which $\sqrt{4 - \sqrt{x^{2}}}$ is defined, lies in the interval

[- 4, 4]

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(- 4, 4]

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(- 4, 4)

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[- 4, 4)

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Solution

The correct option is A $[- 4, 4]$
$\sqrt{4 - \sqrt{x^{2}}} = \sqrt{4 - | x |}$
$\sqrt{4 - | x |}$ is defined when $4 - | x | \geq 0$
When $x \geq 0$
$4 - x \geq 0$
$\Rightarrow x \leq 4 \Rightarrow x \in [0, 4]$

When $x < 0$
$4 + x \geq 0$
$\Rightarrow x \geq - 4 \Rightarrow x \in [- 4, 0)$

$∴ x \in [- 4, 4]$

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Values of x for which √4−√x2 is defined, lies in the interval

The correct option is A [−4,4] √4−√x2=√4−|x| √4−|x| is defined when 4−|x|≥0 When x≥0 4−x≥0 ⇒x≤4 ⇒x∈[0,4] When x<0 4+x≥0 ⇒x≥−4 ⇒x∈[−4,0) ∴x∈[−4,4]

Values of $x$ for which $\sqrt{4 - \sqrt{x^{2}}}$ is defined, lies in the interval