JEE Main 2022MathematicsFunctionsHardMCQ

JEE Main 2022 — Functions Question with Solution

JEE Main 2022 (27 Jul Shift 2)

Question

The domain of the function fx=sin-12x2-3+log2log12x2-5x+5, where t is the greatest integer function, is

Choose an option

Show full solutionCorrect option: C
Correct answer
C1,5-52

Step-by-step explanation

Given fx=sin-12x2-3+log2log12x2-5x+5

For fx to be defined

-1≤2x2-3<1

⇒-1≤2x2-3<2

⇒2<2x2<5

⇒1<x2<52

i.e. x∈-52,-1∪1,52   ...i

and x2-5x+5>0

⇒x-5-52x-5+52>0

i.e. -∞,5-52∪5+52,∞   ...ii

Also log12x2-5x+5>0

⇒x2-5x+5<1

⇒x2-5x+4<0

i.e. x∈1,4   ...iii

From i, ii & iii

So, x∈1,5-52

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About this question

This is a previous-year question from JEE Main 2022, covering the Functions chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.