Question

Given the function f(x)=3x -2 and g(x)= x+2/3 complete parts A and B.

Answer 1

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

$f(x)=3x-2 \enspace g(x)=\frac{x+2}{3}$

(A) $f(g(x))=3(\frac{x+2}{3})-2=x\\g(f(x))=\frac{3x-2+2}{3}=x$

(B) Since $f(g(x))=x$ and $g(f(x))=x$, it holds that

$f(g(x))=g(f(x))$ for all x. This means the composed functions are *identical*

Answer 2

A

f(g(x)) = f($\frac{x+2}{3}$) = 3($\frac{x+2}{3}$) - 2 = x + 2 - 2 = x

g(f(x)) = g(3x - 2) = $\frac{3x-2+2}{3}$ = $\frac{3x}{3}$ = 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