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STD 12 - 2. inverse trigonometric function — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 2. inverse trigonometric function4 Marks
Question
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 :
✓

Answer

c
$ -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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