Compositions of functions

A composition of a function is another way to combine two functions. A composition of a function is usually seen as or .
You read as F of G of X and as G of F of X.
= f(g(x)) and =g(f(x)).
To solve a composition of functions you simply plug g(x) into f(x) and solve.

Here is an example with an explanation:
Solve , where f(x)=x² + 3x and g(x)=x+12
You know that =f(g(x)) so you plug g(x) into f(g(x)) and get f(x+12).
You then solve the equation f(x) =x² + 3x but instead of f(x) you want to use f(g(x)) which we found to be f(x+12).
f(x+12)=(x+12)² +3(x+12) Simply the composition to get a solution
            =x²+24x+144+3x+36
            = x²+27x+180

This works for any set of values for f(x) and g(x), however and do not always produce the same products. In this case f(x) or g(x) will either be a square root or a radical.
For some more information and help check out:
http://www.purplemath.com/modules/fcncomp3.htm
http://www.youtube.com/watch?v=1x7gv3N6FD8

Brandon McCann