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JEE Main 30-Jan-2024 Paper - Shift 1 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 30-Jan-2024 Paper - Shift 14 Marks
MCQ
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 :
  • A
    12
  • B
    9
  • C
    11
  • D
    8
✓

Answer

$-1 \leq\left|\frac{2-|x|}{4}\right| \leq 1$
$\Rightarrow\left|\frac{2-|x|}{4}\right| \leq 1$
$-4 \leq 2-|x| \leq 4$
$-6 \leq-|x| \leq 2$
$-2 \leq|x| \leq 6$
$|x| \leq 6$
$\Rightarrow x \in[-6,6] ...(1)$
Now, $3-x \neq 1$
And $x \neq 2 ...(2)$
and $3-x>0$
$x<3  ...(3)$
From $(1), (2)$ and $(3)$
$\Rightarrow x \in[-6,3-\{2\}]$
$\alpha=6$
$\beta=3$
$\gamma=2$
$\alpha+\beta+\gamma=11$

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