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$9$
- ✓$11$
- D$8$
$ \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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