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Let \( f: R \rightarrow[-1,1] \) is defined by \( f(x)=\sin (2 x+1) \). If domain is restricted to
P
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{ Column-I } & \multicolumn{2}{c|}{ Column-II } \\
\hline (A) & {\( [-3 \pi / 4-1 / 2,-\pi / 2-1 / 2] \)} & (p) & \begin{tabular}{l}
\( f \) is one-one \\
and onto
\end{tabular} \\
\hline (B) & {\( [-3 \pi / 4-1 / 2,-1 / 2] \)} & (q) & \begin{tabular}{l}
\( f \) is one-one \\
but not onto
\end{tabular} \\
\hline (C) & {\( [\pi / 4-1 / 2,3 \pi / 4-1 / 2] \)} & (r) & \begin{tabular}{l}
\( f \) is onto but \\
not one-one
\end{tabular} \\
\hline (D) & {\( \left[-\frac{3 \pi}{4}-\frac{1}{2},-\frac{\pi}{2}-\frac{1}{2}\right] \cup \)} & (s) & \begin{tabular}{l}
\( f \) is neither \\
one-one nor \\
onto
\end{tabular} \\
\hline
\end{tabular}
(1) (A) \( \rightarrow \) (q), (B) \( \rightarrow(\mathrm{r}),(\mathrm{C}) \rightarrow(\mathrm{p}),(\mathrm{D}) \rightarrow(\mathrm{s}) \)
(2) (A) \( \rightarrow \) (s), (B) \( \rightarrow(\mathrm{q}),(\mathrm{C}) \rightarrow(\mathrm{p}),(\mathrm{D}) \rightarrow(\mathrm{r}) \)
(3) (A) \( \rightarrow(\mathrm{p}),(\mathrm{B}) \rightarrow(\mathrm{r}),(\mathrm{C}) \rightarrow(\mathrm{q}),(\mathrm{D}) \rightarrow(\mathrm{r}) \)
(4) (A) \( \rightarrow(\mathrm{r}),(\mathrm{B}) \rightarrow(\mathrm{p}),(\mathrm{C}) \rightarrow(\mathrm{q}),(\mathrm{D}) \rightarrow(\mathrm{s}) \)


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