JEE Main 2016MathematicsFunctionsMediumMCQ

JEE Main 2016 — Functions Question with Solution

JEE Main 2016 (03 Apr)

Question

If fx+2f1x=3x, x≠0, and S=x∈R:fx=f-x, then S

Choose an option

Show full solutionCorrect option: A
Correct answer
AContains exactly two elements

Step-by-step explanation

fx+2. f1x=3x     …1

Replace x by 1x, we get

f1x+2fx=3x      …2

From 1 and 2

3fx=6x-3x

fx=2x-x

∵ fx=f-x

Therefore 2x-x= -2x+x

⇒ 4x=2x

⇒ 2=x2

⇒ x= ± 2

Contains exactly two elements

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About this question

This is a previous-year question from JEE Main 2016, 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.