document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=157496>Question 157496</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I trying to find the inverse of a function. I have to solve for y but I don't know how to do this when there is a variable on the top and bottom.\r<BR>\n" );
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document.write( "x(x-5)= y ---------->  y(y-5)=x  ??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #116059 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=116059\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll start where you left off\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%28y-5%29=x ALIGN=MIDDLE  ALT=\"y%28y-5%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-5y=x ALIGN=MIDDLE  ALT=\"y%5E2-5y=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-5y-x=0 ALIGN=MIDDLE  ALT=\"y%5E2-5y-x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract \"x\" from both sides\r<BR>\n" );
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document.write( "Notice how we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ay%5E2%2Bby%2Bc ALIGN=MIDDLE  ALT=\"ay%5E2%2Bby%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-5 ALIGN=MIDDLE  ALT=\"b=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-x ALIGN=MIDDLE  ALT=\"c=-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So to solve for y, we must use the quadratic formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A%281%29%2A%28-x%29+%29%29%2F%282%2A%281%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-5 ALIGN=MIDDLE  ALT=\"b=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-x ALIGN=MIDDLE  ALT=\"c=-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%285+%2B-+sqrt%28+25%2B4x+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"y+=+%285+%2B-+sqrt%28+25%2B4x+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%285+%2B+sqrt%28+25%2B4x+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"y+=+%285+%2B+sqrt%28+25%2B4x+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%285+-+sqrt%28+25%2B4x+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"y+=+%285+-+sqrt%28+25%2B4x+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the \"plus/minus\"\r<BR>\n" );
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document.write( "So the inverse of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-5%29=+y ALIGN=MIDDLE  ALT=\"x%28x-5%29=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%285+%2B+sqrt%28+25%2B4x+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"y+=+%285+%2B+sqrt%28+25%2B4x+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%285+-+sqrt%28+25%2B4x+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"y+=+%285+-+sqrt%28+25%2B4x+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Note: the inverse of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-5%29=+y ALIGN=MIDDLE  ALT=\"x%28x-5%29=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT a function. </SPAN>\n" );
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