document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=884712>Question 884712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the inverse of f(x)=(4x-2)/(3x+2). Verify your answer by showing that f(f^-1(x))=x and f^-1(f(x))=x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #534606 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=534606\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> see the attached worksheet.<BR>\n" );
document.write( "step 1 is the original equation.<BR>\n" );
document.write( "step 2 interchanges the y and the x.<BR>\n" );
document.write( "step 3 solves for y in the interchanged equation.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "f(x) = (4x-2) / (3x + 2) which is the original equation of f(x).<BR>\n" );
document.write( "g(x) = (-2x-2) / (3x-4) which is the inverse equation.<BR>\n" );
document.write( "you wind up with:<BR>\n" );
document.write( "g(x) = f^-1(x) and f(x) = g^-1(x).<BR>\n" );
document.write( "this is because:<BR>\n" );
document.write( "if a is the inverse of b then b is the inverse of a.\r<BR>\n" );
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document.write( "step 4 shows that f(g(x)) is equal to x.<BR>\n" );
document.write( "step 5 shows that g(f(x)) is equal to x.\r<BR>\n" );
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document.write( "the method of solving f(g(x)) and g(f(x) is to multiply numerator and denominator by the common denominator which removes the fractions and allows you to solve the equations easier.\r<BR>\n" );
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document.write( "that's why step 4 equation is multiplied by (3x-4) / (3x-4) and why step 5 equation is multiplied by (3x + 2) / (3x + 2).\r<BR>\n" );
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document.write( "see below the pictures for additional comments.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/jun2802.jpg\" alt=\"$$$\" </><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/jun2803.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you get f(g(x)) = x and g(f(x)) = x which confirms that the equations are inverses of each other.\r<BR>\n" );
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document.write( "the general idea to find the inverse equatgion is to do steps 1, 2 and 3.<BR>\n" );
document.write( "you replace x with y and y with x and then you solve for  y.<BR>\n" );
document.write( "that's what was done in step 3.\r<BR>\n" );
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