Given that, f(x)=log(∣x∣−2)sin−1(3−x) 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]