Triple Composite Challenge

So far, we have been evaluating composites of two functions, but two is not the limit. Just as an object can be run through three or more machines, you can create a triple composite function or more.

These are evaluated from the inside out just as items like f(g(-2)) are. With the original functions
f(x) = 3x+1, g(x) = 5x² and h(x) = 2x
the triple composite f(g(h(x))) can be evaluated as follows.

1. Find g(h(x)):

g(h(x)) = 5•(h(x))²
             = 5•(2x)²
             = 5•4x²
                = 20x²

2. Take the result of g(h(x)) and plug that into f(x).

f(g(h(x))) = 3(g(h(x)) + 1)
                 = 3•(20x²)
                 = 60x²

Fortunately, you probably will not have to do this very often.