If the domain of the function f(x) = ^ - 1 ((2 - | x |)/(4)) + ( _...

Given:

$y = \cos^{- 1}\left|\dfrac{2 - \left|x\right|}{4}\right| + log{\left(3 - x\right)}^{- 1}$

$⇒ - 1 \le \left|\dfrac{2 - \left|x\right|}{4}\right| \le 1$

$⇒ - 4 \le 2 - \left|x\right| \le 4$

$⇒ - 6 \le - \left|x\right| \le 2$

$⇒ - 2 \le \left|x\right| \le 6$

$⇒ \left|x\right| \le 6$

$⇒ - 6 \le x \le 6 . . . \left(i\right)$

Also, $3 - x > 0\text{and}3 - x \ne 1$

$⇒ x \ne 2 . . . \left(ii\right)$ and $x < 3 . . .\left(iii\right)$

Using \left(i\right), \left(ii\right) \text{and}\left(iii\right)$we get,</p><p>$⇒ x \in [ - 6, 3 ) - \left\{2\right\}

So, on comparing with $x \in [ - \alpha, \beta ) -\left\{\gamma\right\}$ we get,

$⇒ \alpha + \beta + \gamma = 6 + 3 + 2 = 11$