The domain of f(x)=sin-1(3-x)log(x-2) is

Given,f(x)=sin-1(3-x)log(x-2)let g(x)=sin-1(3-x)⇒-1≤3-x≤1 The domain of g(x) is [2,4]Let h(x)=log(x-2)⇒x-2>0 or x>2 and x≠±3⇒x<-2 or x>2∴ Domain  (-∞,-2)∪(2,∞)We know that fg(x)=f(x)g(x),x∈D1∩D2-{x∈R,g(x)=0}Hence the domain of f(x)is (2,4]-{3}i.e (2,3)∪(3,4]