From numerator of the function, we have sin−1(3−x), here −1≤3−x≤1 ⇒−4≤−x≤−2 ⇒2≤x≤4 ...(i) From denominator of the function, we have |x|−2>1 or |x|>3 ⇒x<−3∪x>3...(ii) From both cases, we get the domain of the given function. i.e. 3<x≤4 or x∈(3,4]