How do we perform composition of functions?

Okay well we are all aware of what functions are, right? This is a function --> f(x)=3x+5

That seems easy enough to solve, just plug in a number for x to find f(x). 

Now, here's another function --> g(x)=x+6

It still doesn't look so bad, it's just like the same one, plug in a number for x to find g(x). 

But what if you are asked to find f(g(3))?? :O

                      

                                                WOAH! How do you solve that?

                                                 

Well let's take it step by step and break it down.

First we will need to find out how the equation will look like.

We know that f(x)=3x+5 and g(x)=x+6, so how would f(g(3)) look like?

Well lets start inside the parenthesis --> g(3)=(3)+6 so g(3)=9!

And now we plug the answer of g(3) inside the function f(x) which should be f(9)=3(9)+5. and f(9)=32.

So just remember, whenever you have a composite function just take a deep breath and break it down into steps.

1. Write out what you know, the functions.

2. Start with the inner function, solve it.

3. Replace the x in the outer function with the answer you got from the inner function. 

4. Solve the function.

5. Smile and congratulate yourself on a job well done! :D