Login
Copyright

How to Evaluate Composite Functions

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Manipulating Functions and Solving Equations for Different Variables

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:05 Painting in Art Class
  • 0:58 Defining Composite Functions
  • 1:22 Writing Composite Functions
  • 2:54 Evaluating Composite Functions
  • 4:11 Lesson Summary
Add to Add to Add to

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Login or Sign up

Timeline
Autoplay
Autoplay
Create an account to start this course today
Try it free for 5 days!
Create An Account

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Tyler Cantway

Tyler has tutored math at two universities and has a master's degree in engineering.

Sometimes a math function depends on the outcome of another function. This lesson breaks down this chain reaction, called a composite function, and how to evaluate them.

Painting in Art Class

As part of a school project, Ashley and Brad were painting posters. The posters were white. Ashley had red paint and yellow paint. Brad had blue paint. They each painted many signs. After a while, they were tired of painting by themselves, so they began painting as a team. Ashley handed a white poster to Brad, and he painted it blue. For the next poster, Ashley painted it red and quickly handed it to Brad. When Brad added blue paint to the red paint, the poster became purple. Ashley painted the next poster yellow and gave it to Brad. When Brad added his blue paint, the poster became green.

When each person was painting one color, they got the same answer. But when Ashley painted first and Brad painted second, the final poster might get a completely different color depending on the colors they used.

Defining Composite Functions

In math we have special formulas, called functions, that tell us an answer when we plug in a specific number. However, like the paintings, we can put functions together so that one function gives us a different answer depending on the answer of another. Composite functions use the output of one function as the input of another. This is like a function within a function.

Writing Composite Functions

Let's look at two normal functions: f(x) = x + 2 and g(x) = 3x. If we wanted to make a composite function, we would have to put one function inside the other. To make a composite function where we put g(x) inside the function f(x), we can write it f(g(x)).

Notice that instead of simply putting an x in the function, we substitute the entire g(x) function. When we do that, we have f(g(x)) = (3x) + 2. On the left, you'll see that the g function is inside the f function. On the right, you'll see that instead of the x we substituted 3x.

We can do this other ways too. We could substitute the f function inside the g function. When you put the f function inside the g function, you get g(f(x)) = 3(x+2).

You can even make a composite function of itself. We can make f(f(x)) = (x+2) +2 or g(g(x)) = 3(3x). In each case, we take the whole function and substitute it where we see x.

Evaluating Composite Functions

Now that we've made composite functions, we need to know how to evaluate them. If we were asked to evaluate f(g(5)), we could do this two ways. We could substitute the 5 into the composite function. f(g(5)) = 3*5 + 2

To evaluate this, we do the multiplication first, leaving us f(g(5)) = 15 + 2. This simplifies to 17.

To unlock this lesson you must be a Study.com Member.
Create your account

Register for a free trial

Are you a student or a teacher?
I am a teacher

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back

Earning College Credit

Did you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it free for 5 days!
Create An Account
Support