Online Test Banks
Score higher
See Online Test Banks
Learning anything is easy
Browse Online Courses
Mobile Apps
Learning on the go
Explore Mobile Apps
Dummies Store
Shop for books and more
Start Shopping

How to Break Down a Composition of Functions

A composition of functions is one function acting upon another. Think of it like putting one function inside of the other — f(g(x)), for instance, means that you plug the entire g(x) function in for all x’s in f(x). To solve such a problem, you work from the inside out:

f(g(x)) = f(3x2 – 10) = (3x2 – 10)2 – 6(3x2 – 10) + 1

This process puts the g(x) function into the f(x) function everywhere the f(x) function asks for x. This equation ultimately simplifies to 9x4 – 78x2 + 161, in case you’re asked to simplify the composition (which you usually are).



which easily simplifies to 3(2x – 1) – 10 because the square root and square cancel each other. This equation simplifies even further to 6x – 13.

You may also be asked to find one value of a composed function. To find


for instance, it helps to realize that it’s like reading Hebrew: You work from right to left. In this example, you’re asked to put –3 in for x in f(x), get an answer, and then plug that answer in for x in g(x). Here are these two steps in action:

f(–3) = (–3)2 – 6(–3) + 1 = 28

g(28) = 3(28)2 – 10 = 2,342

  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus

Inside Sweepstakes

Win $500. Easy.