If y=(√(x^2-4))/(cos ^-1(2-x)), then the domain of y is :

We know that

$x^2- 4 ≥ 0$ and $– 1 ≤ 2 – x < 1$

$x^2- 4 ≥ 0$

$⇒x^2≥4$

$|x|≥2$

$x≥2$

$x≤-2$

$– 1 ≤ 2 – x < 1$

so $1 ≤ x ≤3$

⇒ intersection of both of them gives

$2 ≤ x ≤3⇒x∈[2,3]$ domain