Composite Functions

In this lesson I will teach you about composite functions.  If you recall we can perform various operations with functions to include adding, subtracting, multiplying and dividing.  However there is an additional function operation that we use frequently- a composite function.  A word of warning: when students first learn this it can be confusing so watch the lesson as much as you need to until you understand.  Ok back to composite functions.  Basically a composite function is evaluating a function with another function.  Example if I gave you the function f(x) = 4x + 5 and asked you to evaluate it for the value x=3  you would input the value into the function in this manner f(3) = 4(3) + 5. Next you would simplify the expression such that you determine that f(3) = 17.  Now imagine that we had another function like g(x) = 2x – 2 and I asked you to evaluate the f(x) function with the g(x) function- another words plug the g(x) function into the f(x) function just like the previous example with x=3 and simplify- confused?  Don’t worry the lesson will explain how we handle this type of problem and others.  I can’t stress how important composite functions are so take good notes and practice, practice, practice!