SOLUTION: Let f(x) = Ax + B and g(x) = Bx + A, where A does not equal B. If f(g(x)) - g(f(x)) = B - A, what is A + B?

Algebra ->  Functions -> SOLUTION: Let f(x) = Ax + B and g(x) = Bx + A, where A does not equal B. If f(g(x)) - g(f(x)) = B - A, what is A + B?      Log On


   

Question 1090147: Let f(x) = Ax + B and g(x) = Bx + A, where A does not equal B. If f(g(x)) - g(f(x)) = B - A, what is A + B?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28g%29=A%28Bx%2BA%29%2BB=ABx%2BA%5E2%2BB
g%28f%29=B%28Ax%2BB%29%2BA=ABx%2BB%5E2%2BA
So,
f%28g%29-g%28f%29=%28ABx-ABx%29%2BA%5E2%2BB-B%5E2-A
f%28g%29-g%28f%29=A%5E2-B%5E2%2BB-A
It's given that,
f%28g%29-g%28f%29=B-A
So,
A%5E2-B%5E2%2BB-A=B-A
A%5E2-B%5E2=0
%28A-B%29%28A%2BB%29=0
So,
A%2BB=0