Precalculus : Inverse Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #121 : Functions

Find the inverse function of .

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

To find the inverse you must reverse the variables and solve for y.

Reverse the variables:

Solve for y:

Example Question #122 : Functions

Are these two function inverses?   and  .

Possible Answers:

G(x) does not have an inverse.

No

Cannot tell 

Yes

F(x) does not have an inverse.

Correct answer:

Yes

Explanation:

One can ascertain if two functions have an inverse by finding the composition of both functions in turn. Each composition should equal x if the functions are indeed inverses of each other.

The functions are inverses of each other.

Example Question #123 : Functions

Find the inverse of the following equation:

Possible Answers:

Correct answer:

Explanation:

To find the inverse of a function, replace the x any y positions:

Original Equation: 

Inversed Equation:  

Now solve for the inversed y value.

Example Question #124 : Functions

Find the inverse of the following equation:

Possible Answers:

Correct answer:

Explanation:

To find the inverse of a function, replace the x any y positions:

Original Equation: 

Inversed Equation:  

Now solve for the inversed y value.

Example Question #125 : Functions

Find the inverse of the following equation:

Possible Answers:

Correct answer:

Explanation:

To find the inverse of a function, replace the x any y positions:

Original Equation: 

Inversed Equation:  

Now solve for the inversed y value.

Example Question #126 : Functions

Determine the inverse function, given 

 

Possible Answers:

Correct answer:

Explanation:

In order to find the inverse function we 

  1. switch the variables  and 
  2. solve for the new  variable

For the function

 ...

Hence, the inverse function is

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