Chapter 1.5, Problem 10E

Solution

a.

To check: The graph of the relation is a function

  

Given information:

The graph is given below:

  

Concept used:

Vertical line test :The test state that a graph represent a function if and only if all vertical lines intersect the graph at most once.

Explanation:

Here from the graph can understand that when doing the vertical line test ,the vertical line intersect at only one point .So the graph pass in the vertical line test .

Hence the given graph of a relation is afunction.

b.

To check: The relation that have an inverse and is a function .

  

Given information:

The graph is given below.

  

Concept used:

The ordered pair $\left(a,b\right)$ is a relation if only if the ordered pair $\left(b,a\right)$ is an inverse relation.

The inverse of a relation is a function if and only if each horizontal line intersects the graph

of the original relation in at most one point.

Explanations:

Here for each ordered pair $\left(a,b\right)$ has an inverse since its ordered pair $\left(b,a\right)$ is an inverse relation.

But when do the horizontal line test it intersects more than point so it did not the horizontal line test.

Hence this inverse of this relation is not a function.