Algebra 1 : How to find f(x)

Study concepts, example questions & explanations for Algebra 1

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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.

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 #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 #22 : How To Find F(X)

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 #23 : How To Find F(X)

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 #24 : How To Find F(X)

Given 

Find .

Possible Answers:

Correct answer:

Explanation:

which is equal to

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

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 #26 : How To Find F(X)

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 #27 : How To Find F(X)

Given

and

Find

Possible Answers:

Correct answer:

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?

Possible Answers:

6

20

14

25

4

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 #1 : Function Notation

Solve the function for . When 

What does  equal when, 



Possible Answers:

-5

25

0

Correct answer:

Explanation:

Plug 16 in for .  

Add 9 to both sides.  

Take the square root of both sides. =

Final answer is  

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