# Algebra 3/4 : Functions & Relations

## Example Questions

### Example Question #1 : Functions & Relations

Find the composition,  given

Explanation:

To find the composition,  given

recall what a composition of two functions represents.

This means that the function  will replace each  in the function .

Therefore, in this particular problem the composition becomes

### Example Question #2 : Functions & Relations

Find the inverse of .

Explanation:

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function.

For this particular function the inverse is found as follows.

First, switch the variables.

Now, perform algebraic operations to solve for .

Therefore, the inverse is

### Example Question #3 : Functions & Relations

Find the composition,  given

Explanation:

To find the composition,  given

recall what a composition of two functions represents.

This means that the function  will replace each  in the function .

Therefore, in this particular problem the composition becomes

### Example Question #4 : Functions & Relations

Find the inverse of the function .

Explanation:

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function.

For this particular function the inverse is found as follows.

First, switch the variables.

Now, perform algebraic operations to solve for .

Therefore, the inverse is

### Example Question #5 : Functions & Relations

Find the composition,  given

Explanation:

To find the composition,  given

recall what a composition of two functions represents.

This means that the function  will replace each  in the function .

Therefore, in this particular problem the composition becomes

### Example Question #6 : Functions & Relations

Find the composition,  given

Explanation:

To find the composition,  given

recall what a composition of two functions represents.

This means that the function  will replace each  in the function .

Therefore, in this particular problem the composition becomes

### Example Question #7 : Functions & Relations

Find the inverse of .

Explanation:

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function.

For this particular function the inverse is found as follows.

First, switch the variables.

Now, perform algebraic operations to solve for .

Therefore, the inverse is

### Example Question #8 : Functions & Relations

Find the composition,  given

Explanation:

To find the composition,  given

recall what a composition of two functions represents.

This means that the function  will replace each  in the function .

Therefore, in this particular problem the composition becomes

### Example Question #9 : Functions & Relations

Find the inverse of the function .

Explanation:

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function.

For this particular function the inverse is found as follows.

First, switch the variables.

Now, perform algebraic operations to solve for .

Therefore, the inverse is