### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #2 : Linear Algebra

Find the inverse of the following matrix, if possible.

**Possible Answers:**

The inverse does not exist.

**Correct answer:**

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.

**Possible Answers:**

The inverse does not exist.

**Correct answer:**

Write the formula to find the inverse of a matrix.

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

### Example Question #1 : Linear Algebra

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 #1 : 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 #2 : Matrices

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.

### Example Question #1 : Linear Algebra

Find the inverse of the following function.

**Possible Answers:**

**Correct answer:**

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 #1 : Find The Inverse Of A Function

Find the inverse of the following function.

**Possible Answers:**

Does not exist

**Correct answer:**

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 #1 : Find The Inverse Of A Function

Find the inverse of the function.

**Possible Answers:**

**Correct answer:**

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 #1 : Find The Inverse Of A Function

If , what is its inverse function, ?

**Possible Answers:**

**Correct answer:**

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 #1 : Inverses

Find for

**Possible Answers:**

**Correct answer:**

To find the inverse of a function, first swap the x and y in the given function.

Solve for y in this re-written form.