#### Question

State with reason whether following functions have inverse *h*: {2, 3, 4, 5} → {7, 9, 11, 13} with *h* = {(2, 7), (3, 9), (4, 11), (5, 13)}

#### Solution

*h*: {2, 3, 4, 5} → {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*.

∴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}such that *h*(*x*) = *y*.

Thus, *h* is a one-one and onto function. Hence, *h* has an inverse.

Is there an error in this question or solution?

Solution State with Reason Whether Following Functions Have Inverse H: {2, 3, 4, 5} → {7, 9, 11, 13} With H = {(2, 7), (3, 9), (4, 11), (5, 13)} Concept: Composition of Functions and Invertible Function.