GRE Subject Test: Math : Inverses

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

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Example Question #1 : Inverses

Find the inverse of the following matrix, if possible. 

Possible Answers:

The inverse does not exist.

Correct answer:

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 #2 : Inverses

Find the inverse of the following matrix, if possible. 

Possible Answers:

The inverse does not exist.

Correct answer:

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 #3 : Inverse Functions

Find the inverse of the function.

 

Possible Answers:

Correct answer:

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 #3 : Inverses

Find the inverse of the function .

Possible Answers:

Correct answer:

Explanation:

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

Example Question #4 : Inverses

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 #1222 : Pre Calculus

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 #1223 : Pre Calculus

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 #1224 : Pre Calculus

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 #5 : Inverses

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 #1246 : Pre Calculus

Find  for 

Possible Answers:

  

Correct answer:

  

Explanation:

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.

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