If $f(x)=\left\{\begin{matrix}x^3,&x<1\\2x-1,&x≥1\end{matrix}\right.$ and $g(x)=\left\{\begin{matrix}3x,&x≤1\\x^2&x>2\end{matrix}\right.$ then find $(f+g)(x)$.

$\left\{\begin{matrix}x^3+3x,&x<1\\5x-1,&1≤x≤2\\x^2+2x-1,&x>2\end{matrix}\right.$

We have $f(x)=\left\{\begin{matrix}x^3+3x,&x<1\\2x-1,&1≤x≤2\\2x-1,&x>2\end{matrix}\right.$ and $g(x)=\left\{\begin{matrix}3x,&x<1\\3x,&1≤x≤2\\x^2&x>2\end{matrix}\right.$ 

$⇒(f+g)(x)=\left\{\begin{matrix}x^3+3x,&x<1\\2x-1+3x,&1≤x≤2\\2x-1+x^2,&x>2\end{matrix}\right.$

$=\left\{\begin{matrix}x^3+3x,&x<1\\5x-1,&1≤x≤2\\x^2+2x-1,&x>2\end{matrix}\right.$