Precalculus : Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #2 : Linear Algebra

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 #91 : Functions

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 #6 : Find The Inverse Of A Function

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 #1 : 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 #8 : 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 : Inverse Functions

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 #10 : 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:

Example Question #11 : Find The Inverse Of A Function

Find the inverse of .

Possible Answers:

Correct answer:

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 #1232 : Pre Calculus

Find the inverse of .

Possible Answers:

Correct answer:

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 #11 : Find The Inverse Of A Function

Find the inverse of .

Possible Answers:

Correct answer:

Explanation:

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

Switch   and :

We can now solve for :

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