Precalculus : Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #21 : Find The Inverse Of A Function

If , find 

Possible Answers:

Correct answer:

Explanation:

Set , thus .

Now switch  with .

So now, 

.

Simplify to isolate  by itself.

So 

Therefore,

.

Now substitute  with ,

so 

, and 

.

Example Question #31 : Inverse Functions

Find the inverse of this function: 

Possible Answers:

Correct answer:

Explanation:

Write the equation in terms of x and y:

Switch the x and y (this inverts the relationship of the two variables):

Solve for y:

Rewrite to indicate this is the inverse:

Example Question #1 : Inverses

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.

Example Question #111 : Functions

Find the inverse of:  

Possible Answers:

Correct answer:

Explanation:

Interchange the variables and solve for .

Add  on both sides.

Divide by four on both sides.

The answer is:  

Example Question #111 : Functions

Find the inverse function () of the function 

Possible Answers:

None of these answers are correct.

Correct answer:

Explanation:

f(x) can be called y. Switch x and y, and solve for y. The resulting new equation is the inverse of f(x).

 

To double check your work, substitute  into its inverse or vice versa. Both substitutions should equal x.

 

Example Question #11 : Linear Algebra

Which of the following is the inverse of ?

 

Possible Answers:

Correct answer:

Explanation:

Which of the following is the inverse of ?

To find the inverse of a function, we need to swap x and y, and then rearrange to solve for y. The inverse of a function is basically the function we get if we swap the x and y coordinates for every point on the original function.

So, to begin, we can replace the h(x) with y.

Next, swap x and y

Now, we need to get y all by itself; we can to begin by dividng the three over.

Now, recall that 

And that we can rewrite any log as an exponent as follows:

So with that in mind, we can rearrange our function to get y by itself:

Becomes our final answer:

Example Question #31 : Inverse Functions

Find the inverse function of this function: .

Possible Answers:

The inverse of this function is not a function.

Correct answer:

Explanation:

Interchange the variables:

Solve for y:

Because f(x) passes the horizontal line test, its inverse must be a function.

Example Question #31 : Inverse Functions

Find the inverse of the given function:

Possible Answers:

Correct answer:

Explanation:

To find the inverse function, we want to switch the values for domain in range. In other words, switch out the  and  variables in the function:

Example Question #39 : Inverse Functions

Find the inverse of the following function:

Possible Answers:

Correct answer:

Explanation:

To find an inverse, simple switch f(x) and x and then solve for f(x). Thus, the inverse is:

Example Question #32 : Inverse Functions

Find the inverse of the following function:

Possible Answers:

Correct answer:

Explanation:

The inverse of the function  can be found by "reversing" the operations performed on , i.e. subtracting  from the final solution, and then finding the third root of that number, or, in mathematical terms, 

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