Chapter 3, Problem 9PFA

To determine

To find: Which of the following relations is a function.

Answer to Problem 9PFA

  $\left\{\left(3,1\right),\left(-2,-1\right),\left(5,1\right)\right\}$

Explanation of Solution

Concept used:

The relation that defines the set of inputs to the set of outputs is called functions.

In function, each input should have exactly one output.

All functions are relations but all relations are not function.

For Option-A

Given relation is $\left\{\left(3,1\right),\left(-2,-1\right),\left(5,1\right)\right\}$

Here in given relation first elements are $3,-2,5$

As here each input has exactly one output.

Therefore, given relation is a Function.

For Option-B

Given relation is $\left\{\left(2,4\right),\left(-1,2\right),\left(2,-4\right)\right\}$

Here in given relation first elements are $2,-1,2$

Here for input of element $\text{'}2\text{'}$ there are two outputs.

They are $\left\{\left(2,4\right),\left(2,-4\right)\right\}$

As each input doesn’t have exactly one output

So, given relation is not a function.

For Option-C

Given relation is

  $\left\{\left(3,1\right),\left(3,4\right)\left(3,7\right)\right\}$

Here in given relation first elements are $3,3,3$

Here for input element $\text{'}3\text{'}$ there are three outputs.

  $\left\{\left(3,1\right),\left(3,4\right)\left(3,7\right)\right\}$

As each input doesn’t have exactly one output

So, given relation is not a function.

For Option-D

Given relation is

  $\left\{\left(3,1\right),\left(2,1\right)\left(3,-1\right)\right\}$

Here in given relation first elements are $3,2,3$

Here for input element $\text{'}3\text{'}$ there are two outputs.

  $\left\{\left(3,1\right),\left(3,-1\right)\right\}$

As each input doesn’t have exactly one output

So, given relation is not a function.

So, only relation $\left\{\left(3,1\right),\left(-2,-1\right),\left(5,1\right)\right\}$ is the function among given relations.