The domain of definition of the function fx=sin−1⁡(2x)+π6for real-valued x is

For f(x)=sin−1⁡(2x)+π6 to be defined and real, sin−1⁡2x+π/6≥0 or  sin−1⁡2x≥−π6-----(1) But we know that −π/2≤sin−1⁡2x≤π/2 …. (2)Combining (l) and (2),  −π/6≤sin−1⁡2x≤π/2 or  sin⁡(−π/6)≤2x≤sin⁡(π/2) or  −1/2≤2x≤1 or  −1/4≤x≤1/2∴Domain of the function =−14,12