Manipal Entrance Test 2019 Math Paper

Given that, f(x)=

sin−1(3−x)

log(|x|−2)

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]