# GRE Subject Test: Math : Inverses

## Example Questions

### Example Question #1 : Matrices

Find the inverse of the following matrix, if possible.

The inverse does not exist.

Explanation:

Write the formula to find the inverse of a matrix.

Substituting in the given matrix we are able to find the inverse matrix.

### Example Question #1 : Linear Algebra

Find the inverse of the following matrix, if possible.

The inverse does not exist.

Explanation:

Write the formula to find the inverse of a matrix.

Using the given information we are able to find the inverse matrix.

### Example Question #5 : Linear Algebra

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 #6 : Linear Algebra

Find the inverse of the function .

Explanation:

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

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

Find the inverse of the following equation.

.

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.

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.

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 #11 : Inverse Functions

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 #11 : Linear Algebra

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,

.

Find  for