State with reason whether following functions have inverse
(i) `f : {1,2,3,4} ->{10}` with `f = {(1, 10),(2, 10),(3, 10),(4, 10)}`
(ii) `g : {5, 6, 7, 8} to {1,2,3,4}` with `g = {(5, 4),(6, 3),(7, 4),(8, 2)}`
(iii) `h :{2, 3, 4, 5} to {7, 9, 11, 13}` with `h ={(2, 7), (3, 9), (4, 11), (5, 13)}`

Explanation

(i) In `f: {1, 2, 3, 4} to {10}`
`f= {(1, 10), (2, 10), (3, 10), (4, 10)}`
`because f(1) = f(2) = 10`
but `1 ne 2`
Therefore, the inverse of `f` does not exist.
(ii) In ` g: {5, 6, 7, 8} to {1, 2, 3, 4}`
`g= {(5,4 ), (6, 3), (7, 4), (8, 2)}`
`because g (5) = g(7) = 4`
but ` 5 ne 7`
`therefore g` is not one-one.
Therefore, the inverse of g does not exist.
(iii) In `h : {2, 3, 4, 5} to {7, 9, 11, 13}`
`h = {(2, 7), (3, 9), (4, 11), (5, 13)}`
`rArr h (2) = 7, h (3)=9, h (4) = 11, h(5) = 13 `
`rArr ` The inverse of `h` exist and h is one-one onto.