Which of the following relations are functions? Give reasons. In case of a function, find its domain and range.
(i) `f={(1 ,3),(1,5),(2,3),(2,5)}`
(ii) `g={(2,1),(5,1),(8,1),(11,1)}`
(iii) `h={(2,1),(4,2),(6,3),(8,4),(10,5),(12,6)}`

Explanation

(i) `f={(1,3),(1,5),(2,3),(2,5)}`
Here, one element, namely 1 has two images 3 and 5 under f.
`:.` f is not a function.
(ii) `g={(2,1),(5,1),(8,1),(11,1)}`.
Clearly, no two distinct ordered pairs in g have the same first coordinate. So, g is a function.
`:.` dom (g)=[2,5,8,11] and range `g={1}`.
(iii) `h={(2,1),(4,2),(6,3),(8,4),(10,5),(12,6)}`.
Cleardinate, no two distinct ordered pairs in h have the same first coordinate. So, h is a function.
`:.` dom `(h)={2,4,6,8,10,12}` and range `(h)={1,2,3,4,5,6}`.