The domain of f(x)=sin−1⁡log9⁡x2/4  is

We have f(x)=sin−1⁡log9⁡x24 The domain of sin−1⁡x is [−1,1] . Therefore, f(x)=sin−1⁡log9⁡x24   is defined if−1≤log9⁡x24≤1⇒   9−1≤x24≤91⇒     49≤x2≤36⇒   23≤|x|≤6⇒    x∈−6,−23∪23,6 (∵a≤|x|≤b⇔x∈[−b,−a]∪[a,b]) Hence, the domain of f(x) is −6,−23∪23,6 .