Let `S = {1, 2, 3}`. Determine whether the functions `f : S->S`defined as below have inverses. Find `f^(-1)`, if it exists.(a) `f = {(1, 1), (2, 2), (3, 3)}`(b) `f = {(1, 2), (2, 1), (3, 1)}`

Explanation

`s={1,2,3}`

`F:s rightarrow s`

(a)`f={(1,1)(2,2)(3,3)}`

Here f is one one and onto

`therefore f^(-1)` is present
`
F^(-1)={(1,1),(2,2),(3,3)}`

(b)`f={(1,2),(2,1),(3,3)}` here `f(2)= f(3)=1`

`therefore` f is not one one ,hence f is not invertible