# Algebra 1 : How to find f(x)

## 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?

The function does not have an inverse.

The function does not have an inverse.

Explanation:

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?

The function does not have an inverse.

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 #71 : Functions And Lines

Find the inverse of this function.

No inverse exists

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 #24 : How To Find F(X)

Given

Find .

Explanation:

Replacing or substituting  for  in we get

When simplified we get

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

Given

Find .

Explanation:

which is equal to

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

Given .

Find .

Explanation:

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 .

Explanation:

Substituting  in place of  above equation one gets the following:

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

Given

and

Find

Explanation:

### Example Question #1 : Mean

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

4

20

6

25

14

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 #2 : Function Notation

Solve the function for . When

What does  equal when,

25

-5

0