Compositions of Functions

I hope everybody had a great T.A. Day. :) Now let's get back to business

Compositions of a Function is an application of one function to the results of another. It is a way of combining two functions into a simpler function.

This topic is pretty straight forward and by giving you a couple of examples, I think that you'll get it.

Example:

If and , find

First, let's analyse what we are looking for.

There is a logical approach to that equation. You can see that g(x) is inside the f(x). That means that you have to plug inthe g(x) equation to the f(x) to get the answer. Quite confused? Let's try.

So first, insert the "g(x)" into all the (x)'s of the f(x).

Now, put the g(x)) equation instead of "g(x))"

THAT IS IT! You're done! Pretty easy? Told 'ya!

NOTE!Don't be fooled by and ! Most of the time, they are not equal. So be careful!

NOTE #2! What if it just says find ? That means you have to insert the equation that is nearest to the (x) (in this case "g") to the farthest variable. (in this case "f")

So that will become .

Another example? SURE!

If and , find .

Analayse what you are looking for.

In this case you have to plug in f(x) in the g(x) equation to combine the functions.

If you got the answer for this one as . Then you are WRONG! Why?

3x + 2 is a binomial so either you FOIL it or use the formula.

The formula for binomial is:

In this case, 3x is "a" and 2 is "b".

So the answer will be

This is pretty easy stuff so I hope that this helped you. :)