If the domain of the function f(x)=cos -1 (2- x /4 )+ (log e (3-x) ) -1 is [-α, β)-\ y\ , then α+β+γ is equal to :

Mathematics · Functions

JEE Main 2024 — 30 January, Shift 1 — Question 12

If the domain of the function $f(x)=\cos ^{-1}\left(\frac{2-|x|}{4}\right)+\left(\log _{e}(3-x)\right)^{-1}$ is $[-\alpha, \beta)-\{y\}$ , then $\alpha+\beta+\gamma$ is equal to :

Option A:
12
Option B:
9
Option C:
11
Correct
Option D:
8

Answer: C

Step-by-step solution

$-1 \leq\left|\frac{2-|x|}{4}\right| \leq 1$

$\Rightarrow\left|\frac{2-|x|}{4}\right| \leq 1$

$-4 \leq 2-|x| \leq 4$

$-6 \leq-|x| \leq 2$

$-2 \leq|x| \leq 6$

$|x| \leq 6$

$\Rightarrow x \in[-6,6]$

Now, $3-x \neq 1$ And $x \neq 2$ and $3-x>0$ , $x<3$

From (1), (2) and (3)

$\Rightarrow x \in[-6,3)-\{2\}$

$\alpha=6$

$\beta=3$

$\gamma=2$

$\alpha+\beta+\gamma=11$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 30 January, Shift 1
Subject: Mathematics
Chapter: Functions
Topic: Domain & range of functions