The domain of the function f(x)=sin−1⁡(3−x)ln⁡(|x|−2) is

fx =sin-13-xlogx-2  let gx = sin-13-x       then -1≤3-x≤1 ⇒1≥x-3≥-1 ⇒4≥x≥2 ⇒  domain of gx= D1=2,4  let hx =logx-2   then  x-2 >0 ⇒x>2 ⇒ domain of hx=D2=-∞,-2∪2,∞ ⇒domain of fx= D1∩D2-x∈R/ hx=0                                                      = (2, 4] -3                  since hx=0 ⇒ x-2=1⇒x=±3