document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140384>Question 1140384</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please explain:<BR>\n" );
document.write( "Determine whether f(x)=6/(x+5) is one-to-one. If it is one-to-one, find a formula for the inverse. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760906 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=760906\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "In order to show that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is one-to-one, we need to show that if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%5B1%5D%29=f%28x%5B2%5D%29 ALIGN=MIDDLE  ALT=\"f%28x%5B1%5D%29=f%28x%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D=x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "In other words, we need to show that each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > value ONLY has ONE unique <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > value mapping to it. <BR>\n" );
document.write( "In this case, we're assuming that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > are two different values that map to the same <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+ ALIGN=MIDDLE  ALT=\"y+\"   DISABLED_style= \"max-width:90%; height:auto;\" >}value (but as you'll see, they are in fact the same value)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%5B1%5D%29=f%28x%5B2%5D%29 ALIGN=MIDDLE  ALT=\"f%28x%5B1%5D%29=f%28x%5B2%5D%29\"   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=6%2F%28x%5B1%5D%2B5%29=6%2F%28x%5B2%5D%2B5%29 ALIGN=MIDDLE  ALT=\"6%2F%28x%5B1%5D%2B5%29=6%2F%28x%5B2%5D%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   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%2F%28x%5B1%5D%2B5%29=1%2F%28x%5B2%5D%2B5%29 ALIGN=MIDDLE  ALT=\"1%2F%28x%5B1%5D%2B5%29=1%2F%28x%5B2%5D%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .......cross multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B2%5D%2B5%29=%28x%5B1%5D%2B5%29 ALIGN=MIDDLE  ALT=\"%28x%5B2%5D%2B5%29=%28x%5B1%5D%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .......cancel <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   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%5B2%5D=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D=x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So we've shown that if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%5B1%5D%29=f%28x%5B2%5D%29 ALIGN=MIDDLE  ALT=\"f%28x%5B1%5D%29=f%28x%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D=x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is one-to-one.\r<BR>\n" );
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document.write( "now, find a formula for the 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+=+6%2F%28x+%2B+5%29+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+6%2F%28x+%2B+5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >........recall that <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=+6%2F%28x+%2B+5%29+ ALIGN=MIDDLE  ALT=\"y=+6%2F%28x+%2B+5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......swap <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"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=x=+6%2F%28y+%2B+5%29+ ALIGN=MIDDLE  ALT=\"x=+6%2F%28y+%2B+5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........solve for  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"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=x%28y+%2B+5%29+=+6 ALIGN=MIDDLE  ALT=\"x%28y+%2B+5%29+=+6\"   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+%2B+5+=+6%2Fx ALIGN=MIDDLE  ALT=\"y+%2B+5+=+6%2Fx\"   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++=+6%2Fx-5 ALIGN=MIDDLE  ALT=\"y++=+6%2Fx-5\"   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%28x%29+=++6%2Fx-5 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29+=++6%2Fx-5\"   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=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+6%2F%28x%2B5%29%2C+6%2Fx-5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+6%2F%28x%2B5%29%2C+6%2Fx-5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( " </SPAN>\n" );
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