### All Common Core: High School - Functions Resources

## Example Questions

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

Are and inverses of each other?

**Possible Answers:**

Yes

No

**Correct answer:**

Yes

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?

**Possible Answers:**

No

Yes

**Correct answer:**

Yes

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.

Now, add the constants together.

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

Are and inverses of each other?

**Possible Answers:**

No

Yes

**Correct answer:**

Yes

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.

Now add the constants.

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?

**Possible Answers:**

No

Yes

**Correct answer:**

Yes

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.

Now, add the constants together.

Step 3: Is and equal to ?

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?

**Possible Answers:**

Yes

No

**Correct answer:**

Yes

Step 1: Calculate .

Given

can be found as follows.

First distribute the two to both terms in the parentheses.

Now add the constants.

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 ?

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?

**Possible Answers:**

No

Yes

**Correct answer:**

Yes

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.

Now, add the constants together.

Step 3: Is and equal to ?

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?

**Possible Answers:**

No

Yes

**Correct answer:**

No

Step 1: Calculate .

Given

can be found as follows.

Step 2: Calculate .

Step 3: Is and equal to ?

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

### Example Question #71 : Building Functions

Are and inverses of each other?

**Possible Answers:**

No

Yes

**Correct answer:**

No

Step 1: Calculate .

Given

can be found as follows.

Step 2: Calculate .

Step 3: Is and equal to ?

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?

**Possible Answers:**

Yes

No

**Correct answer:**

No

Step 1: Calculate .

Given

can be found as follows.

Now add the constants.

Step 2: Calculate .

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

Step 3: Is and equal to ?

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

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

Are and inverses of each other?

**Possible Answers:**

Yes

No

**Correct answer:**

No

Step 1: Calculate .

Given

can be found as follows.

Now add the constants.

Step 2: Calculate .

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

Step 3: Is and equal to ?

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

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