# Algebra 1 : Functions and Lines

## Example Questions

### Example Question #71 : Functions And Lines

What is the inverse of the function defined by the following set of ordered pairs?

Possible Answers:

The function does not have an inverse.

Correct answer:

Explanation:

The inverse of a function is the relation that switches the positions of the coordinates of each ordered pair. Therefore, the correct choice is

.

### Example Question #3353 : Algebra 1

Find the inverse of this function.

Possible Answers:

No inverse exists

Correct answer:

Explanation:

The inverse of an equation is given by solving for the x value in terms of y. To find the inverse, take the original equation, , and solve for x.

First multiply both sides by (x – 3).

Distribute y into the parenthesis.

Subtract xy to both sides.

Factor the x.

Divide both sides by (1 – y).

Once you have solved for x, switch the x and y terms.

Though an inverse function is found by solving for x, it still must follow the "y=" convention.

### Example Question #3354 : Algebra 1

Given

Find .

Possible Answers:

Correct answer:

Explanation:

Replacing or substituting  for  in we get

When simplified we get

which is the correct answer.

### Example Question #3355 : Algebra 1

Given

Find .

Possible Answers:

Correct answer:

Explanation:

which is equal to

### Example Question #3356 : Algebra 1

Given .

Find .

Possible Answers:

Correct answer:

Explanation:

Given =

Replacing  in the above equation with

one gets

Upon simplification one gets the correct answer which is

### Example Question #76 : Functions And Lines

Given

Find .

Possible Answers:

Correct answer:

Explanation:

Substituting  in place of  above equation one gets the following:

which, after simplification, gives us the correct answer which is

### Example Question #77 : Functions And Lines

Given

and

Find

Possible Answers:

Correct answer:

Explanation:

### Example Question #71 : Functions And Lines

There exists a function f(x) = 3x + 2 for x = 2, 3, 4, 5, and 6. What is the average value of the function?

Possible Answers:

4

20

25

6

14

Correct answer:

14

Explanation:

First we need to find the values of the function: f(2) = 3 * 2 + 2 = 8, f(3) = 11, f(4) = 14, f(5) = 17, and f(6) = 20. Then we can take the average of the five numbers:

average = (8 + 11 + 14 + 17 + 20) / 5 = 14

### Example Question #21 : How To Find F(X)

Solve the function for . When

What does  equal when,

Possible Answers:

-5

0

25

Correct answer:

Explanation:

Plug 16 in for .

Add 9 to both sides.

Take the square root of both sides. =

Final answer is

### Example Question #78 : Functions And Lines

Define  and .

Evaluate .

Possible Answers:

is undefined.

Correct answer:

Explanation:

First evaluate  and , then subtract.