Composition of Functions
The last topic that needs to be discussed in terms of functions and relations is the composition of functions. Let f and g be functions of x (f(x) and g(x)). The composition of f and g is written as and is defined as f(g(x)).
One important note. Make sure not to get multiplication confused with composition. This is a commonly made mistake. Composition is denoted with the symbol while multiplication is denoted with the symbol .
The function is called the composite function. Let’s see how this works.
We are going to work with our two previous functions, f(x) = 2x + 6 and g(x) = 4x – 9.
- Find .
= f(g(x)) = 2(4x – 9) + 6
g(x) is inserted into the x-value of f(x).
= 8x – 18 + 6
= 8x – 12
- Find .
= 4(2x + 6) – 9
f(x) is inserted into the x-value of g(x).
= 8x + 24 – 9
= 8x + 15