If the domain of the function f(x)=log 7 (1-log 4 (x 2 - . . 9 x+18) ) is (α, β) cup(γ, δ) , then α+β+γ+δ is equal to

Mathematics · Functions

JEE Main 2025 — 3 April, Evening Shift — Question 25

If the domain of the function $f(x)=\log _{7}\left(1-\log _{4}\left(x^{2}-\right.\right.$ $9 x+18)$ ) is $(\alpha, \beta) \cup(\gamma, \delta)$ , then $\alpha+\beta+\gamma+\delta$ is equal to

Option A:
17
Option B:
18
Correct
Option C:
15
Option D:
16

Answer: B

Step-by-step solution

$1-\log _{4}\left(x^{2}-9 x+18\right)>0$

$\log _{4}\left(x^{2}-9 x+18\right)<1$

$x^{2}-9 x+18<4$

$x^{2}-9 x+14<0$

$x \in(2,7)$

$x^{2}-9 x+18>0$

$x \in(-\infty, 3) \cup(6, \infty)$

$x \in(2,3) \cup(6,7)$

$\alpha+\beta+\gamma+\delta=18$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 3 April, Evening Shift
Subject: Mathematics
Chapter: Functions
Topic: Domain & range of functions

Let f be a function such that f(x)+3 f (24/x )=4 x , x neq 0 . Then f(3)+f(8) is equal to

Answer: B

Step-by-step solution

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