اگر $f\left( x \right)=\left\{ \begin{matrix}
{{x}^{2}}+2x\,\,\,\,\,\,\,\,\,\,\,\,\,0\le x\le 5 \\
3x+7\,\,\,\,\,\,\,\,\,\,\,\,\,x\gt 5 \\
\end{matrix} \right.$ 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 :
تحلیل ویدئویی تست
محسن ذوالفقاری 
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