JEE Main 2023MathematicsFunctionsMediumMCQ

JEE Main 2023 — Functions Question with Solution

JEE Main 2023 (29 Jan Shift 1)

Question

Let f:R→R be a function such that fx=x2+2x+1x2+1. Then

Choose an option

Show full solutionCorrect option: C
Correct answer
Cfx is one-one in [1,∞) but not in -∞,∞

Step-by-step explanation

Given,

fx=x2+2x+1x2+1

f'(x)=x2+1(2x+2)-(x2+2x+1)2xx2+12

⇒f'(x)=2x3+2x2+2x+2-2x3-4x2-2xx2+12

⇒f'(x)=2(1-x2)x2+12=-2(x+1)(x-1)x2+12

Clearly f(x) is one-one in -∞,-1 and also in (1,∞) but f(x) is not one-one in -∞,∞

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About this question

This is a previous-year question from JEE Main 2023, 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.