ARITHMETIC OPERATIONS ON MULTIVARIABLE FUNCTIONS

Let $D \subseteq ℝ^n$. $f:D\rightarrowℝ^m$ and $g:D\rightarrowℝ^m$ are multivariable functions on $D$, i.e., $n>1$ and $m⩾1$

1. The sum function $f+g$ is defined on $D$ by $(f+g)(x)=f(x)+g(x)$, where $x\in D$.
2. Let $c \in ℝ$. The function $cf$ is defined on $D$ by $(cf)(x)=c\times f(x)$, where $x\in D$.
3. If $m=1$, the product function $fg$ is defined on $D$ by $fg(x)=f(x)\times g(x)$, where $x\in D$.
4. If $m=1$ and $g(x)\ne 0$, the quotient function $f/g$ is defined on $D$ by $( f/g)( x) =$ $\frac{f( x)}{g( x)}$, where $x\in D$.