document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=911269>Question 911269</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for what value(s) will the constant k will the following function NOT be it's own inverse?\r<BR>\n" );
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document.write( "f(x)=(x-k)/(x-1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #553013 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=553013\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Attempting just to find a formula for the inverse, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29=%28x-k%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29=%28x-k%29%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as expected.\r<BR>\n" );
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document.write( "Look at the function definition.  <BR>\n" );
document.write( "x<>1 because f is undefined there.<BR>\n" );
document.write( "x=0 makes for f=k, a constant.<BR>\n" );
document.write( "x=k makes f=0.<BR>\n" );
document.write( "We want to know a certain value for k so that f has either a different inverse or has no inverse.\r<BR>\n" );
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document.write( "k=0, f is just a more specific function.<BR>\n" );
document.write( "k=1, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28k%29=f%281%29=1 ALIGN=MIDDLE  ALT=\"f%28k%29=f%281%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is a constant.\r<BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=1%29 ALIGN=MIDDLE  ALT=\"highlight%28k=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, f will be the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=1 ALIGN=MIDDLE  ALT=\"f%28x%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a HORIZONTAL LINE, the same \"y\" for all values of x.  If  you reflect this over the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x ALIGN=MIDDLE  ALT=\"y=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this forms the inverse RELATION, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This is NOT a function; because it is a VERTICAL LINE, and has infinite values of y for just one value of x.\r<BR>\n" );
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document.write( "<i>For what value(s) will the constant k will the following function NOT be it's own inverse?</i>\r<BR>\n" );
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document.write( "ANSWER:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=1%29 ALIGN=MIDDLE  ALT=\"highlight%28k=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " </SPAN>\n" );
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