document.write( "Question 37903: Determine whether g(x)=3x-6 and f(x)=1/3x+2 are inverse functions.\r
\n" ); document.write( "\n" ); document.write( "Thank you \n" ); document.write( "

Algebra.Com's Answer #23430 by AnlytcPhil(1806) $\"\"$ $\"About$

You can put this solution on YOUR website!

Determine whether g(x)=3x-6 and f(x)=1/3x+2 are inverse functions.
\n" );
document.write( " Thank you\r
\n" );
document.write( "\n" );
document.write( "f(x) and g(x) are inverses if and only if their composition equals the
\n" );
document.write( "identity function I(x) = x.  That is, if\r
\n" );
document.write( "\n" );
document.write( "fog(x) = f(g(x)) = gof(x) = g(f(x)) = x\r
\n" );
document.write( "\n" );
document.write( "===========================================================\r
\n" );
document.write( "\n" );
document.write( "fog(x) = f(g(x)) = f(3x-6) = 1/3(3x-6) + 2 = x - 2 + 2 = x\r
\n" );
document.write( "\n" );
document.write( "That's half of it.\r
\n" );
document.write( "\n" );
document.write( "gof(x) = g(f(x)) = g(1/3x+2)) = 3(1/3x+2) - 6 = x + 6 - 6 = x\r
\n" );
document.write( "\n" );
document.write( "Therefore f(x) and g(x) are inverses.\r
\n" );
document.write( "\n" );
document.write( "Edwin
\n" );
document.write( "   \n" );
document.write( "

\n" );