If \({\rm{f}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{*{20}{c}}{\frac{{{\rm{sin}}\left( {{\rm{p}} + 1} \right){\rm{x}} + {\rm{sinx}}}}{{\rm{x}}},}&{{\rm{x}} < 0}\\{q,}&{x = 0}\\{\frac{{\sqrt {{\rm{x}} + {{\rm{x}}^2}} - \sqrt {\rm{x}} }}{{{{\rm{x}}^{3/2}}}},}&{x > 0}\end{array}} \right.\)is continuous at x = 0, then the ordered pair (p, q) is equal to:

• A. \(\left( { - \frac{3}{2}, - \frac{1}{2}} \right)\)
• B. \(\left( { - \frac{1}{2},\frac{3}{2}} \right)\)
• C. \(\left( { - \frac{3}{2},\frac{1}{2}} \right)\)
• D. \(\left( {\frac{5}{2},\frac{1}{2}} \right)\)