Answer:
[tex](f o g)(x) = 3x + \frac{2}{3}[/tex]
Step-by-step explanation:
We have the function [tex]f(x) = x-\frac{1}{3}[/tex] and we have the function [tex]g(x) = 3x + 1[/tex]. We want to find g(x) composed with f(x)
Then, the function (f o g)(x) is the same since f(g(x))
That is, you must do x = g(x) and then enter g(x) into the function f(x).
[tex]f(g(x)) = (g(x)) -\frac{1}{3}[/tex]
[tex]f(g(x)) = (3x + 1) -\frac{1}{3}[/tex]
Simplifying, we obtain:
[tex](f o g)(x) = 3x + 1 -\frac{1}{3}\\\\(f o g)(x) = 3x + \frac{2}{3}[/tex]
Finally. The composite function is:
[tex](f o g)(x) = 3x + \frac{2}{3}[/tex]
