# Precalculus : Find the Inverse of a Function

## Example Questions

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

Find the inverse of,

.

Possible Answers:

Correct answer:

Explanation:

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:

Explanation:

First, switch the variables making  into .

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

### Example Question #3 : Find The Inverse Of A Function

Find the inverse of the following equation.

.

Possible Answers:

Correct answer:

Explanation:

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.

### Example Question #4 : Find The Inverse Of A Function

Find the inverse of the following function.

Possible Answers:

Correct answer:

Explanation:

To find the inverse of y, or

first switch your variables x and y in the equation.

Second, solve for the variable  in the resulting equation.

Simplifying a number with 0 as the power, the inverse is

### Example Question #5 : Find The Inverse Of A Function

Find the inverse of the following function.

Possible Answers:

Does not exist

Correct answer:

Explanation:

To find the inverse of y, or

first switch your variables x and y in the equation.

Second, solve for the variable  in the resulting equation.

And by setting each side of the equation as powers of base e,

### Example Question #11 : Inverse Functions

Find the inverse of the function.

Possible Answers:

Correct answer:

Explanation:

To find the inverse we need to switch the variables and then solve for y.

Switching the variables we get the following equation,

.

Now solve for y.

### Example Question #7 : Find The Inverse Of A Function

Find the inverse of

Possible Answers:

Correct answer:

Explanation:

So we first replace every  with an  and every  with a .

Our resulting equation is:

Now we simply solve for y.

Subtract 9 from both sides:

Now divide both sides by 10:

The inverse of

is

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

What is the inverse of

Possible Answers:

Correct answer:

Explanation:

To find the inverse of a function we just switch the places of all  and  with eachother.

So

turns into

Now we solve for

Divide both sides by

### Example Question #11 : Linear Algebra

If , what is its inverse function, ?

Possible Answers:

Correct answer:

Explanation:

We begin by taking  and changing the  to a , giving us .

Next, we switch all of our  and , giving us .

Finally, we solve for  by subtracting  from each side, multiplying each side by , and dividing each side by , leaving us with,

.

### Example Question #9 : Find The Inverse Of A Function

Find the inverse of .

Possible Answers:

Correct answer:

Explanation:

To find the inverse of the function, we switch the switch the  and  variables in the function.

Switching  and  gives

Then, solving for  gives our answer: