If the domain of the function sin -1 (3 x-22/2 x-19 )+log e (frac 3 x 2 -8 x+5 x 2 -3 x-10 ) is (α, β] , then 3 α+10 β is equal to :

Mathematics · Functions

JEE Main 2024 — 4 April, Shift 1 — Question 18

If the domain of the function $\sin ^{-1}\left(\frac{3 x-22}{2 x-19}\right)+\log _{e}\left(\frac{3 x^{2}-8 x+5}{x^{2}-3 x-10}\right)$ is $(\alpha, \beta]$ , then $3 \alpha+10 \beta$ is equal to :

Option A:
97
Correct
Option B:
100
Option C:
95
Option D:
98

Answer: A

Step-by-step solution

$-1 \leq \frac{3 x-22}{2 x-19} \leq 1 \quad$

$\frac{3 x^{2}-8 x+5}{x^{2}-3 x-10}>0$

$x \in\left(5, \frac{41}{5}\right]$

$3 \alpha+10 \beta=97$

Answer key and solution verified before publishing.

Practise Functions

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2024
Paper: 4 April, Shift 1
Subject: Mathematics
Chapter: Functions
Topic: Domain & range of functions

Let the sum of the maximum and the minimum values of the function f(x)=frac2 x^2-3 x+82 x^2+3 x+8 be m/n , where gcd(m, n)=1 . Then m+n is…

Answer: A

Step-by-step solution

Practise Functions

More Functions questions from this paper