Discussion
The domain of the function \(f(x) = 2\sin^{-1}(2x - 1) - \frac{\pi}{4}\) is
Answer: B
The domain is [0,1].
\(\sin^{-1}u\) is defined only for \(-1 \leq u \leq 1\). With \(u = 2x - 1\):
\[ \begin{aligned} -1 \leq 2x - 1 &\leq 1 \\ 0 \leq 2x &\leq 2 \\ 0 \leq x &\leq 1 \end{aligned} \]
The constant \(-\frac{\pi}{4}\) and the factor 2 do not affect the domain. [-1,1] is the domain of \(\sin^{-1}x\) itself, and [0,2] forgets to divide by 2.
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