document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113795>Question 113795</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the inverse of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%2Fx ALIGN=MIDDLE  ALT=\"f%28x%29=2%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82811 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=82811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%2Fx ALIGN=MIDDLE  ALT=\"f%28x%29=2%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2Ff%28x%29 ALIGN=MIDDLE  ALT=\"x=2%2Ff%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Switch the variables x and f(x)\r<BR>\n" );
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document.write( "Now let's solve for f(x)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Af%28x%29=2 ALIGN=MIDDLE  ALT=\"x%2Af%28x%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by f(x)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%2Fx ALIGN=MIDDLE  ALT=\"f%28x%29=2%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by x to solve for f(x)\r<BR>\n" );
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document.write( "Now this may seem a bit odd, but the inverse of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%2Fx ALIGN=MIDDLE  ALT=\"f%28x%29=2%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > is itself: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%2Fx ALIGN=MIDDLE  ALT=\"f%28x%29=2%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%2Fx ALIGN=MIDDLE  ALT=\"f%28x%29=2%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2Cx%2C+2%2Fx%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2Cx%2C+2%2Fx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > note: the red line should be a dotted line\r<BR>\n" );
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document.write( "and we can see that if we reflect the curve over the red line we'll get the same line (in other words the curve folds over \r<BR>\n" );
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document.write( "itself). So this visually verifies our answer </SPAN>\n" );
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