The solution set of the inequation $|[|x

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

The solution set of the inequation $|[|x|-7]| -5<0$ is ([.] denotes the greatest integer function)

Options:

$[3, 12)$

$(-12, -3]$

$(-12, 12)$

$(-12, -3]∪[3,12)$

Correct Answer:

$(-12, -3]∪[3,12)$

Explanation:

We have,

$|[|x|-7]| -5<0$

$⇒|[|x|-7]| <5$

$⇒-5<[|x|-7] <5$

$⇒-4≤|x|-7 <5$

$⇒3≤|x|<12 ⇒ x ∈(−12, – 3] ∪[3,12)$