JEE Main 2023MathematicsFunctionsMediumMCQ

JEE Main 2023 — Functions Question with Solution

JEE Main 2023 (06 Apr Shift 1)

Question

Let 5fx+4f1x=1x+3, x>0. Then 18∫12fxdx is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C10 loge2-6

Step-by-step explanation

Given:

5fx+4f1x=1x+3   ....1

Replace x→1x

5f1x+4fx=x+3   ....2

Eliminating f1x from 1 & 2, we get

9fx=5x+15-4x-12

⇒9fx=5x-4x+3

⇒18fx=10x-8x+6

⇒18∫12fxdx=∫1210x-8x+6dx

⇒18∫12fxdx=10logx-4x2+6x12

⇒18∫12fxdx=10log2-4-10log1+2

⇒18∫12fxdx=10loge2-6

Hence this is the correct option.

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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.