If the domain of the function $f(x) = \log_e\left(\frac{2x+3}{4x^2+x-3}\right) + \cos^{-1}\left(\frac{2x-1}{x+2}\right)$ is $(\alpha, \beta]$, then the value of $5\beta - 4\alpha$ is equal to

JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 30 January 2024, Shift 2, Maths Q1

Question 1 of 90 in this shift, Maths question 1 of 30, Section A.

If the domain of the function

f(x) = \log_e\left(\frac{2x+3}{4x^2+x-3}\right) + \cos^{-1}\left(\frac{2x-1}{x+2}\right)

(\alpha, \beta]

, then the value of

5\beta - 4\alpha

is equal to

(1) $9$
(2) $10$
(3) $11$
(4) $12$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Relations and Functions
Topic: Functions and Domain
Idea tested: Intersection of Domains

Same idea in other shifts

Asked 3× in all

4 Aug 2021, Shift 2 · Q61The domain of the function $f(x)=\frac{\log_2(x+3)}{(x+1)(x+2)}$ isEasySingle correct
18 Mar 2021, Shift 1 · Q61If the functions are defined as $f(x)=\sqrt{x}$ and $g(x)=\sqrt{1-x}$ , then what is the common domain of the following functions :…EasySingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.