Question

Function s is the set of points: {(4,3),(5,3), (8,6), (9,6),(12,9), (13,9)}.

(a) What is the inverse of function s?
(b) Is the inverse of function s a function? Explain your answer.

Answer 1

(a) {(3,4),(3,5), (6,8), (6,9),(9,12), (9,13)}

(b) The inverse relation is not a function

Explanation:

Inverse Function

If a relation is given as a set of points (x,y), the inverse relation will have the same points with its coordinates switched.

The relation is given as the set:

{(4,3),(5,3), (8,6), (9,6),(12,9), (13,9)}

(a) The inverse relation is:

{(3,4),(3,5), (6,8), (6,9),(9,12), (9,13)}

(b)

A relation is a function if each element of the input set is related to one and only one element of the output set.

The inverse relation is not a function because several points don't meet the above condition. For example, (3,4) and (3,5) relate the element 3 with two elements.