### All Algebra 1 Resources

## Example Questions

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

A function is defined by the following set of ordered pairs:

What is its inverse?

**Possible Answers:**

The function does not have an inverse.

**Correct answer:**

The function does not have an inverse.

The inverse of a function is the relation that switches the positions of the coordinates of each ordered pair. However, for a function to have an inverse, the result of those switches must itself be a function. The switches yield the relation

which is not a function, since the -coordinate 5 is paired with two -coordinates, 1 and 5.

### Example Question #22 : How To Find F(X)

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:**

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 #71 : Functions And Lines

Find the inverse of this function.

**Possible Answers:**

No inverse exists

**Correct answer:**

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 #24 : How To Find F(X)

Given

Find .

**Possible Answers:**

**Correct answer:**

Replacing or substituting for in we get

When simplified we get

which is the correct answer.

### Example Question #25 : How To Find F(X)

Given

Find .

**Possible Answers:**

**Correct answer:**

which is equal to

### Example Question #26 : How To Find F(X)

Given .

Find .

**Possible Answers:**

**Correct answer:**

Given =

Replacing in the above equation with

one gets

Upon simplification one gets the correct answer which is

### Example Question #27 : How To Find F(X)

Given

Find .

**Possible Answers:**

**Correct answer:**

Substituting in place of above equation one gets the following:

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

### Example Question #28 : How To Find F(X)

Given

and

Find

**Possible Answers:**

**Correct answer:**

### Example Question #1 : Mean

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

**Possible Answers:**

4

20

6

25

14

**Correct answer:**

14

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 #2 : Function Notation

Solve the function for . When

What does equal when,

**Possible Answers:**

25

-5

0

**Correct answer:**

Plug 16 in for .

Add 9 to both sides.

Take the square root of both sides. =

Final answer is

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