The domain of |x−$$2$$|−$$1+3$$−|x−$$2$$| is

Correct option is 4[−1,1]∪[3,5]

Questions

$The domain of \sqrt{| x - 2 | - 1} + \sqrt{3 - | x - 2 |} is$

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[−1,3]∪[5,∞)

[−1,5]

[1,3]

[−1,1]∪[3,5]

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detailed solution

Correct option is D

We must have |x−2|≥1 and |x−2|≤3 If a≤|x|≤b⇔x∈[−b,−a]∪[a,b] From 1≤|x−2|≤3 it implies (x−2)∈[−3,−1]∪[1,3]⇔ x∈[−1,1]∪[3,5]

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The domain of |x−2|−1+3−|x−2| is

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$The domain of \sqrt{| x - 2 | - 1} + \sqrt{3 - | x - 2 |} is$