Let $f=\{(1,6),(2,5),(4,3),(5,2),(8,-1),(10,-3)\}$ and $g=\{(2,0),(3,2),(5,6)$,(7,10),(8,12),(10,16)\}$
Find (i) dom (f $+g$ ) (ii) dom $\left(\frac{f}{g}\right)$.
Given, $f=\{(1,6),(2,5),(4,3),(5,2),(8,-1),(10,-3)\}$
$g=\{(2,0),(3,2),(5,6),(7,10),(8,12),(10,16)\}$
(1) Domain of $f=\{1,2,4,5,8,10\}$
Domain of $\mathrm{g}=\{2,3,5,7,8,10\}$
Domain of $(f+g)=\{x: x \in D f \cap D g\}$
Where Df = Domain of function f, Dg = Domain of function g
Domain of $(f+g)=\{2,5,8,10\}$.
(2) Domain of quotient function $\mathrm{f} / \mathrm{g}=\{\mathrm{x}: \mathrm{x} \in \mathrm{D} \mathrm{f} \cap \mathrm{Dg}$ and $\mathrm{g}(\mathrm{x}) \neq 0\}$
Domain of (f/g) = {2,5,8,10}.
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