document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #704545 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"f%28g%29=A%28Bx%2BA%29%2BB=ABx%2BA%5E2%2BB\"$
\n" ); document.write( " $\"g%28f%29=B%28Ax%2BB%29%2BA=ABx%2BB%5E2%2BA\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"f%28g%29-g%28f%29=%28ABx-ABx%29%2BA%5E2%2BB-B%5E2-A\"$
\n" ); document.write( " $\"f%28g%29-g%28f%29=A%5E2-B%5E2%2BB-A\"$
\n" ); document.write( "It's given that,
\n" ); document.write( " $\"f%28g%29-g%28f%29=B-A\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"A%5E2-B%5E2%2BB-A=B-A\"$
\n" ); document.write( " $\"A%5E2-B%5E2=0\"$
\n" ); document.write( " $\"%28A-B%29%28A%2BB%29=0\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"A%2BB=0\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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