document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166996>Question 166996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm working with a student myself at a Deaf school in Jamaica and we came across a problem that stumped me. The question is:\r<BR>\n" );
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document.write( "If f(x)=2x-3, then find the value of f^-1(0)\r<BR>\n" );
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document.write( "The part that stumps me is putting f to the power of -1. <BR>\n" );
document.write( "We understand how to solve the problem if it's not but to a power.<BR>\n" );
document.write( "Thank you so much for your help! I appreciate it greatly. <BR>\n" );
document.write( "-Isaac </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123032 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123032\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Isaac, it's not a power but it stands for the inverse function. <BR>\n" );
document.write( "For example, if I have a function <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;\" > such that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=5 ALIGN=MIDDLE  ALT=\"f%281%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then the inverse function, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > would be such that when I plug in x=5, I would get back y=1. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%285%29=1 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%285%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "1.To find the inverse, first change to x,y notation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2Ax-3 ALIGN=MIDDLE  ALT=\"y=2%2Ax-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then interchange the positions of x and y and solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%29=sqrt%282%2Ahighlight%28y%29-3%29 ALIGN=MIDDLE  ALT=\"highlight%28x%29=sqrt%282%2Ahighlight%28y%29-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2y-3 ALIGN=MIDDLE  ALT=\"x=2y-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=x%2B3 ALIGN=MIDDLE  ALT=\"2y=x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B3%29%2F2 ALIGN=MIDDLE  ALT=\"y=%28x%2B3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >}<BR>\n" );
document.write( "The solution for the new y is the inverse function.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29=%28x%2B3%29%2F2 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29=%28x%2B3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let's try it. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x-3 ALIGN=MIDDLE  ALT=\"f%28x%29=2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=2%281%29-3=2-3=-1 ALIGN=MIDDLE  ALT=\"f%281%29=2%281%29-3=2-3=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now when I plug in x=-1 into the inverse function, <BR>\n" );
document.write( "I should get back y=1.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29=%28x%2B3%29%2F2 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29=%28x%2B3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28-1%29=%28-1%2B3%29%2F2 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28-1%29=%28-1%2B3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28-1%29=2%2F2 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28-1%29=2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28-1%29=1 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28-1%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You interested at the value of the inverse function for x=0.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29=%28x%2B3%29%2F2 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29=%28x%2B3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%280%29=%280%2B3%29%2F2 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%280%29=%280%2B3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%280%29=3%2F2 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%280%29=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You could have also solved it by asking what x makes my original function equal to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3=0 ALIGN=MIDDLE  ALT=\"2x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=3 ALIGN=MIDDLE  ALT=\"2x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The inverse functions interchange x and y values.<BR>\n" );
document.write( "Hopefully that makes sense. Good luck!  </SPAN>\n" );
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