document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162043>Question 1162043</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the function f(x)=-2c+cx-x^2 and f^-1(3)=-1, find c </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #785728 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=785728\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-2c%2Bcx-x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29=-2c%2Bcx-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%283%29=-1 ALIGN=MIDDLE  ALT=\"f%5E-1%283%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "first find inverse\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=y ALIGN=MIDDLE  ALT=\"f%28x%29=y\"   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=-2c%2Bcx-x%5E2 ALIGN=MIDDLE  ALT=\"y=-2c%2Bcx-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...swap variables\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2c%2Bcy-y%5E2 ALIGN=MIDDLE  ALT=\"x=-2c%2Bcy-y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........complete square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2c%2B%28b%5E2%2Bcy-y%5E2%29-b%5E2 ALIGN=MIDDLE  ALT=\"x=-2c%2B%28b%5E2%2Bcy-y%5E2%29-b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=c%2F2 ALIGN=MIDDLE  ALT=\"b=c%2F2\"   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=x=-2c%2B%28%28c%2F2%29%5E2%2Bcy-y%5E2%29-%28c%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"x=-2c%2B%28%28c%2F2%29%5E2%2Bcy-y%5E2%29-%28c%2F2%29%5E2\"   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=x%2B2c%2B%28c%2F2%29%5E2+=%28c%2F2-y%29%5E2 ALIGN=MIDDLE  ALT=\"x%2B2c%2B%28c%2F2%29%5E2+=%28c%2F2-y%29%5E2\"   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=x%2B2c%2Bc%5E2%2F4+=%28c%2F2-y%29%5E2 ALIGN=MIDDLE  ALT=\"x%2B2c%2Bc%5E2%2F4+=%28c%2F2-y%29%5E2\"   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=sqrt%28x%2B2c%2Bc%5E2%2F4%29+=c%2F2-y ALIGN=MIDDLE  ALT=\"sqrt%28x%2B2c%2Bc%5E2%2F4%29+=c%2F2-y\"   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=+c%2F2-sqrt%28x%2B2c%2Bc%5E2%2F4%29 ALIGN=MIDDLE  ALT=\"y=+c%2F2-sqrt%28x%2B2c%2Bc%5E2%2F4%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=f%5E-1=+c%2F2-sqrt%28x%2B2c%2Bc%5E2%2F4%29 ALIGN=MIDDLE  ALT=\"f%5E-1=+c%2F2-sqrt%28x%2B2c%2Bc%5E2%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%283%29=-1 ALIGN=MIDDLE  ALT=\"f%5E-1%283%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, means if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   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=-1=+c%2F2-sqrt%283%2B2c%2Bc%5E2%2F4%29 ALIGN=MIDDLE  ALT=\"-1=+c%2F2-sqrt%283%2B2c%2Bc%5E2%2F4%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=sqrt%283%2B2c%2Bc%5E2%2F4%29=+c%2F2%2B1 ALIGN=MIDDLE  ALT=\"sqrt%283%2B2c%2Bc%5E2%2F4%29=+c%2F2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >....square both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B2c%2Bc%5E2%2F4=+%28c%2F2%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"3%2B2c%2Bc%5E2%2F4=+%28c%2F2%2B1%29%5E2\"   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=3%2B2c%2Bc%5E2%2F4=+c%5E2%2F4%2B2%28c%2F2%29%2B1 ALIGN=MIDDLE  ALT=\"3%2B2c%2Bc%5E2%2F4=+c%5E2%2F4%2B2%28c%2F2%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >....simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B2c=+c%2B1 ALIGN=MIDDLE  ALT=\"3%2B2c=+c%2B1\"   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=2c-c=1-3 ALIGN=MIDDLE  ALT=\"2c-c=1-3\"   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=c=-2 ALIGN=MIDDLE  ALT=\"c=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-2c%2Bcx-x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29=-2c%2Bcx-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is\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%28-2%29%2B%28-2%29x-x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29=-2%28-2%29%2B%28-2%29x-x%5E2\"   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=f%28x%29=4-2x-x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29=4-2x-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29+ ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >will be\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1=+-2%2F2-sqrt%28x-4%2B1%29 ALIGN=MIDDLE  ALT=\"f%5E-1=+-2%2F2-sqrt%28x-4%2B1%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=f%5E-1=+-1-sqrt%28x-3%29+ ALIGN=MIDDLE  ALT=\"f%5E-1=+-1-sqrt%28x-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> check result if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1=+-1 ALIGN=MIDDLE  ALT=\"f%5E-1=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1=+-1-sqrt%283-3%29 ALIGN=MIDDLE  ALT=\"-1=+-1-sqrt%283-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1=+-1-sqrt%280%29 ALIGN=MIDDLE  ALT=\"-1=+-1-sqrt%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1=+-1 ALIGN=MIDDLE  ALT=\"-1=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >->true\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );