What is the domain of the function $f(x)=\frac{\sin^{-1}(3-x)}{\log(|x|-2)}$?

(2, 3) ∪ (3, 4]

$f(x)=\frac{\sin^{-1}(3-x)}{\log(|x|-2)}$

Let $g(x)=\sin^{-1}(3-x)$

$-1≤3-x≤1$

Domain of g(x) is [2, 4] and let $h(x)=\log[|x|-2]$

$|x|-2 > 0$

$|x|>2$

$(-∞, -2)∪(2,∞)$

We know that $(\frac{f}{g})(x)=\frac{f(x)}{g(x)}∀\,x∈D1∩D2-\{x∈R:g(x)=0\}$

Domain of $f(x)=(2,4]-\{3\}=(2, 3) ∪ (3, 4]$