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Which of the following relations are fun...

Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.
(i) {(2,1),(5,1),(8,1),(11,1),(14,1),(17,1)}
(ii) {(2,1),(4,2),(6,3),(8,4),(10,5),(12,6),(14,7)}
(iii) {(1,3),(1,5),(2,5)}

Text Solution

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The correct Answer is:
N/a
Let `R_(1)={(2,1),(5,1),(8,1),(11,1),(14,1),(17,1)}`
Find components of any two ordered pairs of `R_(1)` are not equal, so `R_(1)` is a function.
(ii) Let `R_(2)={(2,1),(4,2),(6,3),(8,4),(10,5),(12,6),(14,7)}`
First components of any two ordered pairs of `R_(2)` are not equal, so `R_(2)` is a function.
(iii) Let `R_(3)={(1,3),(1,5),(2,5)}`
First components of two ordered paire (1,3) and (1,5) of `R_(3)` are equal. So, `R_(3)` is not a function.
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