اگر f(x)={x2+2x0≤x≤53x+7x>5 و g\left( x \right)=\left\{ \begin{matrix} 2{{x}^{2}}-x\,\,\,\,\,\,\,\,\,\,\,\,\,0\le x\le 10 \\ -2x+4\,\,\,\,\,\,\,\,\,\,\,\,\,x\gt 10 \\ \end{matrix} \right. باشد، ضابطهی تابع \left( f+g \right)\left( x \right) کدام است؟
1 )
\left\{ \begin{matrix} 3{{x}^{2}}+4x+11\,\,\,\,\,\,\,\,\,\,\,\,\,0\le x\le 5 \\ \begin{align} & {{x}^{2}}+4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5\lt x\le 10 \\ & x+11\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\gt 10 \\ \end{align} \\ \end{matrix} \right.
2 )
\left\{ \begin{matrix} 3{{x}^{2}}+x\,\,\,\,\,\,\,\,\,\,\,\,\,0\le x\le 5 \\ x+11\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\gt 5 \\ \end{matrix} \right.
3 )
\left\{ \begin{matrix} 3{{x}^{2}}+x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\le x\le 5 \\ \begin{align} & {{x}^{2}}+4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5\lt x\le 10 \\ & x+11\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\gt 10 \\ \end{align} \\ \end{matrix} \right.
\left\{ \begin{matrix} 3{{x}^{2}}+x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\le x\le 5 \\ \begin{align} & 2{{x}^{2}}+2x+7\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5\lt x\le 10 \\ & x+11\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\gt 10 \\ \end{align} \\ \end{matrix} \right.
پاسخ تشریحی :
محسن ذوالفقاری 
