Composite Functions

Let w(x) represent the result of combining f(x) and g(x) into the composition function g(f(x)).
Let f(x) = 3x – 7 and g(x) = -2x + 4.
The goal will be to find the function equation for w(x).

Start by inputting an x-value into the f equation.
Take the output, or f(x), and use it as input into the g equation.
The resulting output is the output of the w equation, or g(f).

For example, let’s start with x = 3.
Then f = 3(3) – 7 = 2. Now put f(x) = 2 into g (note f(x) replaces x in this equation) and get = -2(2) + 4 = 0.
This means that w(x) will contain (3,0), where 3 is the original input and 0 is the final output.
Use a spreadsheet and generate several ordered pairs until you see a pattern that will help you write the function equation for w(x).