College Algebra & Trigonometry, 2018a

226 CHAPTER 4. FUNCTIONS
4.7 Composite functions
Similar to the way in which we used transformations to analyze the equation of
a function, it is sometimes helpful to consider a given function as being several
functions of the variable combined together.
For example, instead of thinking of the function f(x) =(2x − 7) 3 as being a single
function, we can think of it as being two functions:
g(x) =2x − 7
and
h(x) =x 3
Then f(x) is the combination or “composition” of these two functions together.
The first function multiplies the variable by 2, and subtracts 7 from the result. The
second function takes this answer and raises it to the third power. The notation
for the composition of functions is an open circle: ◦.
In the example above we would say that the function f(x) =(2x − 7) 3 is equivalent
to the composition h ◦ g(x) or h(g(x)). The order of function composition is
important. The function g ◦ h(x) would be equivalent to g(h(x)), which would be
equal to g(x 3 )=2(x 3 ) − 7=2x 3 − 7.