# Precalculus : Find the Inverse of a Relation

## Example Questions

### Example Question #1 : Find The Inverse Of A Relation

What is the inverse function of

?

Explanation:

To find the inverse function of

we replace the  with  and vice versa.

So

Now solve for

### Example Question #2 : Inverse Functions

Find the inverse of the function.

Explanation:

To find the inverse function, first replace  with :

Now replace each  with an  and each  with a :

Solve the above equation for :

Replace  with . This is the inverse function:

### Example Question #3 : Inverse Functions

Find the inverse of the function.

Explanation:

To find the inverse function, first replace  with :

Now replace each  with an  and each  with a :

Solve the above equation for :

Replace  with . This is the inverse function:

### Example Question #2 : Find The Inverse Of A Relation

Find the inverse of the function .

Explanation:

To find the inverse of , interchange the  and  terms and solve for .

### Example Question #4 : Inverse Functions

What point is the inverse of the ?

Explanation:

When trying to find the inverse of a point, switch the x and y values.

So

### Example Question #5 : Inverse Functions

What is the inverse of ?

Explanation:

When trying to find the inverse of a point, switch the x and y values.

So,

### Example Question #6 : Inverse Functions

Find the inverse of the following function:

Explanation:

In order to find the inverse of the function, we need to switch the x- and y-variables.

After switching the variables, we have the following:

Now solve for the y-variable. Start by subtracting 10 from both sides of the equation.

Divide both sides of the equation by 4.

Rearrange and solve.