If \(\sin^{-1}(2x - 1) = -\displaystyle\frac{\pi}{6}\), then x is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{1}{4}\)
Since \(-\frac{\pi}{6}\) lies in \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\), the definition of \(\sin^{-1}\) gives
\( \displaystyle 2x - 1 = \sin\left(-\frac{\pi}{6}\right) \)
\( \displaystyle 2x - 1 = -\frac{1}{2} \)
\( \displaystyle 2x = \frac{1}{2} \)
\( \displaystyle x = \frac{1}{4} \)