# Precalculus : Inverse Functions

## Example Questions

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

Find the inverse of the following function.

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 #2 : Find The Inverse Of A Function

Find the inverse of the following function.

Does not exist

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 #3 : Find The Inverse Of A Function

Find the inverse of the function.

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 #4 : Find The Inverse Of A Function

Find the inverse of

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 #5 : Find The Inverse Of A Function

What is the inverse of

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 #6 : Find The Inverse Of A Function

If , what is its inverse function, ?

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 #7 : Find The Inverse Of A Function

Find the inverse of .

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:

### Example Question #11 : Find The Inverse Of A Function

Find the inverse of .

Explanation:

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

Switching  and  gives:

Solving for  yields our final answer:

### Example Question #12 : Find The Inverse Of A Function

Find the inverse of .

Explanation:

To find the inverse of the function, we can switch   and  in the function and solve for :

Switching   and  gives:

Solving for  yields our final answer:

### Example Question #13 : Find The Inverse Of A Function

Find the inverse of .