If =x^{2}+2 \) and =\sqrt{\boldsymbol{x}+\mathbf{1}} \) then (\boldsymbol{x}) \)

If \( f: R^{+} \rightarrow R^{+}, f(x)=x^{2}+2 \) and \( g: \) \( \boldsymbol{R}^{+} \rightarrow \boldsymbol{R}^{+}, \boldsymbol{g}(\boldsymbol{x})=\sqrt{\boldsymbol{x}+\mathbf{1}} \) then \( (\boldsymbol{f}+\boldsymbol{g})(\boldsymbol{x}) \) equals

• A. \( \sqrt{x^{2}+3} \)
• B. \( x+3 \)
• C. \( \sqrt{x^{2}+2}+(x+1) \)
• D. \( x^{2}+2+\sqrt{(x+1)} \)