Given the function f(x)=3x -2 and g(x)= x+2/3 complete parts a and b. a. find f(g(x)) and g(f( include your work in your final answer. b. use complete sentence's to explain the relationship that exists between the composition of the functions. f(g(x)) and g(f(

First, I should point out that g(x) should be written as g(x)=(x+2)/3, otherwise the problem is confusing.  

(A)

(B) Since and , it holds that

for all x. This means the composed functions are *identical*

A

f(g(x)) = f() = 3() - 2 = x + 2 - 2 = x

g(f(x)) = g(3x - 2) = = = x

B

Since both composite functions f(g(x)) and g(f(x)) equal x

This indicates that the functions f(x) and g(x) are inverse functions

y = - 6

step-by-step explanation:

given the point (- 2, y) lies on the graph then it is a solution of it's equation.

substitute x = - 2 into the equation for value of y

y = 3(- 2) = 3 × - 2 = - 6

the point on the graph is (- 2, 6)