Question

State with reason whether given function has inverse:
(i) h:{2,3,4,5} $\to$ {7,9,11,13}with h={(2,7),(3,9),(4,11),(5,13)}

Answer 1

Function h:{2,3,4,5} $\to$ {7,9,11,13} defined as h={(2,7),(3,9),(4,11),(5,13)}
It is seen that all distinct elements of the set {2,3,4,5} have distinct images under h. Therefore, function h is one-one.
Also, h is onto, since for every element y of the set {7,9,11,13}, there exists an element x in the set {2,3,4,5} have distinct images under h. Thus, h is a one -one and onto function. Hence, h has an inverse.