Algebra 3/4 : Algebra 3/4

Study concepts, example questions & explanations for Algebra 3/4

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Example Questions

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Example Question #1 : Algebra 3/4

Find the composition,  given

Possible Answers:

Correct answer:

Explanation:

To find the composition,  given

recall what a composition of two functions represents.

This means that the function  will replace each  in the function .

Therefore, in this particular problem the composition becomes

Example Question #1 : Functions & Relations

Find the inverse of .

Possible Answers:

Correct answer:

Explanation:

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function. 

For this particular function the inverse is found as follows.

First, switch the variables.

Now, perform algebraic operations to solve for .

Therefore, the inverse is

Example Question #1 : Functions & Relations

Find the composition,  given

Possible Answers:

Correct answer:

Explanation:

To find the composition,  given

recall what a composition of two functions represents.

This means that the function  will replace each  in the function .

Therefore, in this particular problem the composition becomes

Example Question #2 : Functions & Relations

Find the inverse of the function .

Possible Answers:

Correct answer:

Explanation:

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function. 

For this particular function the inverse is found as follows.

First, switch the variables.

Now, perform algebraic operations to solve for .

Therefore, the inverse is

Example Question #2 : Algebra 3/4

Find the composition,  given

Possible Answers:

Correct answer:

Explanation:

To find the composition,  given

recall what a composition of two functions represents.

This means that the function  will replace each  in the function .

Therefore, in this particular problem the composition becomes

Example Question #3 : Functions & Relations

Find the composition,  given

Possible Answers:

Correct answer:

Explanation:

To find the composition,  given

recall what a composition of two functions represents.

This means that the function  will replace each  in the function .

Therefore, in this particular problem the composition becomes

Example Question #4 : Functions & Relations

Find the inverse of .

Possible Answers:

Correct answer:

Explanation:

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function. 

For this particular function the inverse is found as follows.

First, switch the variables.

Now, perform algebraic operations to solve for .

Therefore, the inverse is

Example Question #1 : Functions & Relations

Find the composition,  given

Possible Answers:

Correct answer:

Explanation:

To find the composition,  given

recall what a composition of two functions represents.

This means that the function  will replace each  in the function .

Therefore, in this particular problem the composition becomes

Example Question #5 : Functions & Relations

Find the inverse of the function .

Possible Answers:

Correct answer:

Explanation:

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function. 

For this particular function the inverse is found as follows.

First, switch the variables.

Now, perform algebraic operations to solve for .

Therefore, the inverse is

Example Question #1 : Algebra 3/4

Simplify the following radical expression.

Possible Answers:

Correct answer:

Explanation:

To simplify the radical expression look at the factors under each radical.

Recall that 25 and 4 are perfect squares.

From here 12 can be factored further.

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