Correct option is (b) \((2,3) \cup(3,4]\)
\(f(x)=\frac{\sin ^{-1}(3-x)}{\ln (|x|-2)}\)
Using domain for \(\sin ^{-1} \mathrm{x}\)
\(\Rightarrow-1 \leq 3-x \leq 1 \)
\(-1 \leq x-3 \leq 1 \)
\( 2 \leq x \leq 4\)
Using domain for \(\ln (|\mathrm{x}|-2)\)
\( \Rightarrow \ln (|x|-2) \# 0 \)
\( |x|-2 \neq 1\)
\( |x| \neq 3\)
\( x \neq 3,-3\)
Also, \((|x|-2)>0\)
\( |x|>2 \)
\( x>2, x<-2\)
Now taking intersection, we get
\( x \in(2,4]-\{3\} \text { or } \)
\(x \in(2,3) \cup(3,4]\)
