Question

Given the functions, f(x) =3x -2 and g(x) = x+2/3, complete parts 1 and 2.

Find f(g(x)) and g(f(x)). Include your work in your final answer. Use complete sentences to explain the relationship that exists between the composition of the functions, f(g(x)) and g(f(x)).

Answer 1

f(g(x)) = 3(x+2/3) - 2
Now, distribute the 3:
3x + 2 - 2
f(g(x)) = 3x
g(f(x)) = (3x - 2) + 2/3
Get a common denominator to add the faction
-6/3 + 2/3
g(f(x)) = 3x - 4/3

The relationship between the two composition functions is that they are commutative or permutable.