The domain of the functionf(x)=sin−1⁡log2⁡12x2 is

For f (x) to be defined, we must have−1≤log2⁡12x2≤1⇒2−1≤12x2≤21 [∵the base=2>1]⇒1≤x2≤4                ........ (1)  Now,  1≤x2⇒x2−1≥0 i.e. (x−1)(x+1)≥0 ⇒ x≤−1 or x≥1      ........ (2)  Also, x2≤4⇒x2−4≤0 i.e. (x−2)(x+2)≤0 ⇒−2≤x≤2              ........ (3)From Eq. (2) and (3), we get the domain of f=((−∞,−1]∪[1,∞))∩[−2,2] =[−2,−1]∪[1,2]