The domain of definition of the function
\[
f(x)=\sqrt{\sin ^{-1}(2 x)+\frac{\pi}{6}}
\]
for rea...
The domain of definition of the function
\[
f(x)=\sqrt{\sin ^{-1}(2 x)+\frac{\pi}{6}}
\]
for real-valued \( x \) is
(A) \( \left[-\frac{1}{4}, \frac{1}{2}\right] \)
(B) \( \left[-\frac{1}{2}, \frac{1}{2}\right] \)
(C) \( \left(-\frac{1}{2}, \frac{1}{9}\right) \)
(D) \( \left[-\frac{1}{4}, \frac{1}{4}\right] \)
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