### All Precalculus Resources

## Example Questions

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

What is the inverse function of

?

**Possible Answers:**

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

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 #4 : Inverse Functions

Find the inverse of the function .

**Possible Answers:**

**Correct answer:**

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

### Example Question #5 : Inverse Functions

What point is the inverse of the ?

**Possible Answers:**

**Correct answer:**

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

So

### Example Question #6 : Inverse Functions

What is the inverse of ?

**Possible Answers:**

**Correct answer:**

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

So,

### Example Question #1 : Inverse Functions

Find the inverse of the following function:

**Possible Answers:**

**Correct answer:**

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.

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

Find the inverse of,

.

**Possible Answers:**

**Correct answer:**

In order to find the inverse, switch the x and y variables in the function then solve for y.

Switching variables we get,

.

Then solving for y to get our final answer.

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

Find the inverse of,

.

**Possible Answers:**

**Correct answer:**

First, switch the variables making into .

Then solve for y by taking the square root of both sides.

### Example Question #1 : Linear Algebra

Find the inverse of the following equation.

.

**Possible Answers:**

**Correct answer:**

To find the inverse in this case, we need to switch our x and y variables and then solve for y.

Therefore,

becomes,

To solve for y we square both sides to get rid of the sqaure root.

We then subtract 2 from both sides and take the exponenetial of each side, leaving us with the final answer.