SOLUTION: Let f(x) = 3x+2 and g(x) = 2x+A. Find a value for A so that f(g(x)) = g(f(x)). Note: Do not use spaces in your answers. When possible, answers should be in this format: x+A

Algebra ->  Test -> SOLUTION: Let f(x) = 3x+2 and g(x) = 2x+A. Find a value for A so that f(g(x)) = g(f(x)). Note: Do not use spaces in your answers. When possible, answers should be in this format: x+A      Log On


   

Question 1121005: Let f(x) = 3x+2 and g(x) = 2x+A.
Find a value for A so that f(g(x)) = g(f(x)).
Note: Do not use spaces in your answers. When possible, answers should be
in this format: x+A+1
Answer:
f(g(x)) = Answer
g(f(x)) = Answer
A = Answer
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Let f(x) = 3x+2 and g(x) = 2x+A.  
Find a value for A so that f(g(x)) = g(f(x)).

Note: Do not use spaces in your answers.  When possible, answers should be
in this format: x+A+1

Answer:

f(g(x)) = f(2x+A) = 3(2x+A)+2 = 6x+3A+2

g(f(x)) = g(3x+2) = 2(3x+2)+A = 6x+4+A = 6x+A+4

f(g(x)) = g(f(x))

6x+3A+2 = 6x+4+A
   3A+2 = 4+A
     2A = 2
      A = 1 

Edwin