Which of the following relations are functions? If it is a functi… - Vidyadip

Question

Which of the following relations are functions? If it is a function determine its domain and range.
(i) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5) (12, 6), (14, 7)}
(ii) {(0, 0), (1, 1), (1, -1), (4, 2), (4, -2), (9, 3), (9, -3), (16, 4), (16, -4)}
(iii) {(1, 1), (3, 1), (5, 2)}

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Answer

(i) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5) (12, 6), (14, 7)}

Every element of set $\mathrm{A}$ has been assigned a unique element in set $\mathrm{B}$.
$\therefore$ Given relation is a function.
$
\begin{aligned}
& \text { Domain }=\{2,4,6,8,10,12,14\}, \\
& \text { Range }=\{1,2,3,4,5,6,7\}
\end{aligned}
$
(ii) $\{(0,0),(1,1),(1,-1),(4,2),(4,-2),(9,3),(9,-3),(16,4),(16,-4)\}$
$\therefore(1,1),(1,-1) \in$ the relation
$\therefore$ Given relation is not a function.
As element 1 of the domain has not been assigned a unique element of co-domain.
(iii) $\{(1,1),(3,1),(5,2)\}$Every element of set A has been assigned a unique element in set B.
∴ Given relation is a function.
Domain = {1, 3, 5}, Range = {1, 2}

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