# Common Core: High School - Functions : Inverse Functions Verified Through Composition: CCSS.Math.Content.HSF-BF.B.4b

## Example Questions

### Example Question #1 : Inverse Functions Verified Through Composition: Ccss.Math.Content.Hsf Bf.B.4b

Are  and  inverses of each other?

Yes

No

Yes

Explanation:

This question is testing one's ability to calculation of the composition of functions for the purpose of verifying inverse functions. It is important to recall that there are two compositions of functions that need to be calculated before two functions are verified as inverses.

For the purpose of Common Core Standards, verify by composition that one function is the inverse of another, falls within the Cluster B of build new functions from existing functions concept (CCSS.Math.content.HSF.BF.B).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Calculate .

Given

can be found as follows.

First distribute the two in the numerator to the fraction.

Now multiply the one in the denominator by  and add the two terms in the denominator together.

From here, multiple the numerator by the reciprocal of the denominator.

The  in the numerator and in the denominator cancel out as does the two.

Step 2: Calculate .

First multiply the two in the denominator by  and then add the terms.

Now, multiply the numerator by the reciprocal of the denominator.

The  and the two cancel out.

Step 3: Is  and  equal to ?

In order for two functions to be the inverse of one another the composition of their functions must equal . This is due to the fact that evaluating a function at the inverse function value are opposite operations and will cancel out to leave just .

Since both  and  equal to  they are inverse functions of each other.

### Example Question #2 : Inverse Functions Verified Through Composition: Ccss.Math.Content.Hsf Bf.B.4b

Are  and  inverses of each other?

No

Yes

Yes

Explanation:

This question is testing one's ability to calculation of the composition of functions for the purpose of verifying inverse functions. It is important to recall that there are two compositions of functions that need to be calculated before two functions are verified as inverses.

For the purpose of Common Core Standards, verify by composition that one function is the inverse of another, falls within the Cluster B of build new functions from existing functions concept (CCSS.Math.content.HSF.BF.B).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Calculate .

Given

can be found as follows.

First drop the parentheses.

Now simplify by adding the constant terms together.

Step 2: Calculate .

First drop the parentheses.

Step 3: Is  and  equal to ?

In order for two functions to be the inverse of one another the composition of their functions must equal . This is due to the fact that evaluating a function at the inverse function value are opposite operations and will cancel out to leave just .

Since both  and  equal to  they are inverse functions of each other.

### Example Question #3 : Inverse Functions Verified Through Composition: Ccss.Math.Content.Hsf Bf.B.4b

Are  and  inverses of each other?

No

Yes

Yes

Explanation:

This question is testing one's ability to calculation of the composition of functions for the purpose of verifying inverse functions. It is important to recall that there are two compositions of functions that need to be calculated before two functions are verified as inverses.

For the purpose of Common Core Standards, verify by composition that one function is the inverse of another, falls within the Cluster B of build new functions from existing functions concept (CCSS.Math.content.HSF.BF.B).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Calculate .

Given

can be found as follows.

First distribute the two to both terms in the parentheses.

Step 2: Calculate .

First factor out a two from the numerator and denominator.

Now, drop the parentheses and add the constants.

Step 3: Is  and  equal to ?

In order for two functions to be the inverse of one another the composition of their functions must equal . This is due to the fact that evaluating a function at the inverse function value are opposite operations and will cancel out to leave just .

Since both  and  equal to  they are inverse functions of each other.

### Example Question #4 : Inverse Functions Verified Through Composition: Ccss.Math.Content.Hsf Bf.B.4b

Are  and  inverses of each other?

Yes

No

Yes

Explanation:

This question is testing one's ability to calculation of the composition of functions for the purpose of verifying inverse functions. It is important to recall that there are two compositions of functions that need to be calculated before two functions are verified as inverses.

For the purpose of Common Core Standards, verify by composition that one function is the inverse of another, falls within the Cluster B of build new functions from existing functions concept (CCSS.Math.content.HSF.BF.B).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Calculate .

Given

can be found as follows.

First drop the parentheses.

Now simplify by adding the constant terms together.

Step 2: Calculate .

First drop the parentheses.

Step 3: Is  and  equal to ?

In order for two functions to be the inverse of one another the composition of their functions must equal . This is due to the fact that evaluating a function at the inverse function value are opposite operations and will cancel out to leave just .

Since both  and  equal to  they are inverse functions of each other.

### Example Question #5 : Inverse Functions Verified Through Composition: Ccss.Math.Content.Hsf Bf.B.4b

Are  and  inverses of each other?

Yes

No

Yes

Explanation:

This question is testing one's ability to calculation of the composition of functions for the purpose of verifying inverse functions. It is important to recall that there are two compositions of functions that need to be calculated before two functions are verified as inverses.

For the purpose of Common Core Standards, verify by composition that one function is the inverse of another, falls within the Cluster B of build new functions from existing functions concept (CCSS.Math.content.HSF.BF.B).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Calculate .

Given

can be found as follows.

First distribute the two to both terms in the parentheses.

Step 2: Calculate .

First factor out a two from the numerator and denominator.

Now, drop the parentheses and add the constants.

Step 3: Is  and  equal to ?

In order for two functions to be the inverse of one another the composition of their functions must equal . This is due to the fact that evaluating a function at the inverse function value are opposite operations and will cancel out to leave just .

Since both  and  equal to  they are inverse functions of each other.

### Example Question #6 : Inverse Functions Verified Through Composition: Ccss.Math.Content.Hsf Bf.B.4b

Are  and  inverses of each other?

No

Yes

Yes

Explanation:

This question is testing one's ability to calculation of the composition of functions for the purpose of verifying inverse functions. It is important to recall that there are two compositions of functions that need to be calculated before two functions are verified as inverses.

For the purpose of Common Core Standards, verify by composition that one function is the inverse of another, falls within the Cluster B of build new functions from existing functions concept (CCSS.Math.content.HSF.BF.B).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Calculate .

Given

can be found as follows.

First drop the parentheses.

Now simplify by adding the constant terms together.

Step 2: Calculate .

First drop the parentheses.

Step 3: Is  and  equal to ?

In order for two functions to be the inverse of one another the composition of their functions must equal . This is due to the fact that evaluating a function at the inverse function value are opposite operations and will cancel out to leave just .

Since both  and  equal to  they are inverse functions of each other.

### Example Question #7 : Inverse Functions Verified Through Composition: Ccss.Math.Content.Hsf Bf.B.4b

Are  and  inverses of each other?

Yes

No

No

Explanation:

This question is testing one's ability to calculation of the composition of functions for the purpose of verifying inverse functions. It is important to recall that there are two compositions of functions that need to be calculated before two functions are verified as inverses.

For the purpose of Common Core Standards, verify by composition that one function is the inverse of another, falls within the Cluster B of build new functions from existing functions concept (CCSS.Math.content.HSF.BF.B).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Calculate .

Given

can be found as follows.

Step 2: Calculate .

Step 3: Is  and  equal to ?

In order for two functions to be the inverse of one another the composition of their functions must equal . This is due to the fact that evaluating a function at the inverse function value are opposite operations and will cancel out to leave just .

Since  and  are not equal to  they are not inverse functions of each other.

### Example Question #8 : Inverse Functions Verified Through Composition: Ccss.Math.Content.Hsf Bf.B.4b

Are  and  inverses of each other?

No

Yes

No

Explanation:

This question is testing one's ability to calculation of the composition of functions for the purpose of verifying inverse functions. It is important to recall that there are two compositions of functions that need to be calculated before two functions are verified as inverses.

For the purpose of Common Core Standards, verify by composition that one function is the inverse of another, falls within the Cluster B of build new functions from existing functions concept (CCSS.Math.content.HSF.BF.B).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Calculate .

Given

can be found as follows.

Step 2: Calculate .

Step 3: Is  and  equal to ?

In order for two functions to be the inverse of one another the composition of their functions must equal . This is due to the fact that evaluating a function at the inverse function value are opposite operations and will cancel out to leave just .

Since  and  are not equal to  they are not inverse functions of each other.

### Example Question #9 : Inverse Functions Verified Through Composition: Ccss.Math.Content.Hsf Bf.B.4b

Are  and  inverses of each other?

Yes

No

No

Explanation:

This question is testing one's ability to calculation of the composition of functions for the purpose of verifying inverse functions. It is important to recall that there are two compositions of functions that need to be calculated before two functions are verified as inverses.

For the purpose of Common Core Standards, verify by composition that one function is the inverse of another, falls within the Cluster B of build new functions from existing functions concept (CCSS.Math.content.HSF.BF.B).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Calculate .

Given

can be found as follows.

Step 2: Calculate .

Multiply the one by three over three to get a common denominator.

Step 3: Is  and  equal to ?

In order for two functions to be the inverse of one another the composition of their functions must equal . This is due to the fact that evaluating a function at the inverse function value are opposite operations and will cancel out to leave just .

Since both  and  are not equal to  they are not inverse functions of each other.

### Example Question #10 : Inverse Functions Verified Through Composition: Ccss.Math.Content.Hsf Bf.B.4b

Are  and  inverses of each other?

Yes

No

No

Explanation:

This question is testing one's ability to calculation of the composition of functions for the purpose of verifying inverse functions. It is important to recall that there are two compositions of functions that need to be calculated before two functions are verified as inverses.

For the purpose of Common Core Standards, verify by composition that one function is the inverse of another, falls within the Cluster B of build new functions from existing functions concept (CCSS.Math.content.HSF.BF.B).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Calculate .

Given

can be found as follows.

Step 2: Calculate .

Multiply the one by two over two to get a common denominator.

Step 3: Is  and  equal to ?

In order for two functions to be the inverse of one another the composition of their functions must equal . This is due to the fact that evaluating a function at the inverse function value are opposite operations and will cancel out to leave just .

Since both  and  are not equal to  they are not inverse functions of each other.