document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208167>Question 1208167</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the rational function f(x) = (x + 2)/(x - 2), find the inverse. \r<BR>\n" );
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document.write( "Let me see.\r<BR>\n" );
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document.write( "Let f(x) = y\r<BR>\n" );
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document.write( "y = (x + 2)/(x - 2)\r<BR>\n" );
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document.write( "x = (y + 2)/(y - 2)\r<BR>\n" );
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document.write( "Stuck here.... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846390 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=846390\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "f(x) = (x+2)/(x-2)<BR>\n" );
document.write( "y = (x+2)/(x-2)<BR>\n" );
document.write( "x = (y+2)/(y-2) .... swap x and y; solve for y<BR>\n" );
document.write( "x(y-2) = y+2<BR>\n" );
document.write( "xy-2x = y+2<BR>\n" );
document.write( "xy-y = 2+2x<BR>\n" );
document.write( "y(x-1) = 2x+2<BR>\n" );
document.write( "y = (2x+2)/(x-1)<BR>\n" );
document.write( "g(x) = (2x+2)/(x-1)\r<BR>\n" );
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document.write( "g(x) is the inverse of f(x), and vice versa.<BR>\n" );
document.write( "To verify, you need to show that, <BR>\n" );
document.write( "f( g(x) ) = x and g( f(x) ) = x<BR>\n" );
document.write( "for all x in the domain. I'll leave this verification for the student to do.<BR>\n" );
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