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

## Example Questions

### Example Question #61 : Building Functions

Find the inverse of .

**Possible Answers:**

**Correct answer:**

This question is testing one's ability to algebraically calculate the inverse of a given function. This also builds one's understanding of the concept of a function and its inverse at a basic level, graphing functions, and the Cartesian plane and its coordinate system.

For the purpose of Common Core Standards, finding the inverse of a simple function, 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: Switch the and variables.

The given function is,

recall that therefore,

.

Now switch the variables.

Step 2: Solve for .

Solving for requires the use of algebraic operations to move constants from side to side. Remember to use the opposite operation to move a constant from one side to the other.

Step 3: Answer the question.

Recall that after the variable are switch, and is solved for it is really the inverse of that is being solved for thus, .

### Example Question #1 : Simple Functions And Coresponding Inverses: Ccss.Math.Content.Hsf Bf.B.4a

Find the inverse of .

**Possible Answers:**

**Correct answer:**

This question is testing one's ability to algebraically calculate the inverse of a given function. This also builds one's understanding of the concept of a function and its inverse at a basic level, graphing functions, and the Cartesian plane and its coordinate system.

For the purpose of Common Core Standards, finding the inverse of a simple function, 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: Switch the and variables.

The given function is,

recall that therefore,

.

Now switch the variables.

Step 2: Solve for .

Solving for requires the use of algebraic operations to move constants from side to side. Remember to use the opposite operation to move a constant from one side to the other.

Step 3: Answer the question.

Recall that after the variable are switch, and is solved for it is really the inverse of that is being solved for thus, .

### Example Question #63 : Building Functions

Find the inverse of .

**Possible Answers:**

**Correct answer:**

This question is testing one's ability to algebraically calculate the inverse of a given function. This also builds one's understanding of the concept of a function and its inverse at a basic level, graphing functions, and the Cartesian plane and its coordinate system.

For the purpose of Common Core Standards, finding the inverse of a simple function, 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: Switch the and variables.

The given function is,

recall that therefore,

.

Now switch the variables.

Step 2: Solve for .

Solving for requires the use of algebraic operations to move constants from side to side. Remember to use the opposite operation to move a constant from one side to the other.

Step 3: Answer the question.

Recall that after the variable are switch, and is solved for it is really the inverse of that is being solved for thus, .

### Example Question #64 : Building Functions

Find the inverse of .

**Possible Answers:**

**Correct answer:**

Step 1: Switch the and variables.

The given function is,

recall that therefore,

.

Now switch the variables.

Step 2: Solve for .

Step 3: Answer the question.

### Example Question #1 : Simple Functions And Coresponding Inverses: Ccss.Math.Content.Hsf Bf.B.4a

Find the inverse of .

**Possible Answers:**

**Correct answer:**

Step 1: Switch the and variables.

The given function is,

recall that therefore,

.

Now switch the variables.

Step 2: Solve for .

Step 3: Answer the question.

### Example Question #66 : Building Functions

Find the inverse of .

**Possible Answers:**

**Correct answer:**

Step 1: Switch the and variables.

The given function is,

recall that therefore,

.

Now switch the variables.

Step 2: Solve for .

Step 3: Answer the question.

### Example Question #67 : Building Functions

Find the inverse of .

**Possible Answers:**

**Correct answer:**

Step 1: Switch the and variables.

The given function is,

recall that therefore,

.

Now switch the variables.

Step 2: Solve for .

Step 3: Answer the question.

### Example Question #68 : Building Functions

Find the inverse of .

**Possible Answers:**

**Correct answer:**

Step 1: Switch the and variables.

The given function is,

recall that therefore,

.

Now switch the variables.

Step 2: Solve for .

Step 3: Answer the question.

### Example Question #69 : Building Functions

Find the inverse of .

**Possible Answers:**

**Correct answer:**

Step 1: Switch the and variables.

The given function is,

recall that therefore,

.

Now switch the variables.

Step 2: Solve for .

Step 3: Answer the question.

### Example Question #70 : Building Functions

Find the inverse of .

**Possible Answers:**

**Correct answer:**

Step 1: Switch the and variables.

The given function is,

recall that therefore,

.

Now switch the variables.

Step 2: Solve for .

Step 3: Answer the question.

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