JEE Main 2022MathematicsFunctionsMediumMCQ

JEE Main 2022 — Functions Question with Solution

JEE Main 2022 (28 Jul Shift 1)

Question

Considering only the principal values of the inverse trigonometric functions, the domain of the function fx=cos-1x2-4x+2x2+3 is

Choose an option

Show full solutionCorrect option: B
Correct answer
B-14,∞

Step-by-step explanation

Given,

fx=cos-1x2-4x+2x2+3

We know that domain of cos-1 is -1,1

So, x2+4x+2x2+3≤1

⇒x2-4x+22≤x2+32

⇒x2-4x+22-x2+32≤0

⇒2x2-4x+5-4x-1≤0

Since 2x2-4x+5>0 as its discriminant D<0

So, -4x-1≤0⇒x≥-14

⇒x∈[-14,∞)

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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.