document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=919877>Question 919877</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x) is a function such that f(1)=2, f(4)=3, f(7)=4, f^-1(x) is the inverse of f(x),what is  f^-1(f^-1(3))? Thank you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558034 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=558034\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
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;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=2 ALIGN=MIDDLE  ALT=\"f%281%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > => means if <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;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >;it's point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%284%29=3 ALIGN=MIDDLE  ALT=\"f%284%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > => means if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >;it's point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"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%287%29=4 ALIGN=MIDDLE  ALT=\"f%287%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> means if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >;it's point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42 ALIGN=MIDDLE  ALT=\"42\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "use these points to find what <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 equal to\r<BR>\n" );
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document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=change_this_name10094.solver>Find the equation of line going through points</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (1, 2) and (x2, y2) = (7, 4).<BR>\n" );
document.write( "  Slope a is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%284-2%29%2F%287-1%29+=+0.333333333333333 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  Intercept is found from equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ax%5B1%5D%2Bb+=+y%5B1%5D ALIGN=MIDDLE  ALT=\"a%2Ax%5B1%5D%2Bb+=+y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.333333333333333%2A1+%2Bb+=+1.66666666666667 ALIGN=MIDDLE  ALT=\"0.333333333333333%2A1+%2Bb+=+1.66666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" >. From that, <BR>\n" );
document.write( "  intercept b is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=y%5B1%5D-a%2Ax%5B1%5D ALIGN=MIDDLE  ALT=\"b=y%5B1%5D-a%2Ax%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2-0.333333333333333%2A1+=+1.66666666666667 ALIGN=MIDDLE  ALT=\"b=2-0.333333333333333%2A1+=+1.66666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  y=(0.333333333333333)x + (1.66666666666667)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Your graph:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++drawing%28600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2C%0D%0A++++graph%28+600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2C+0.333333333333333%2Ax%2B1.66666666666667+%29%2C%0D%0A++++red%28+locate%28+1%2C+2%2C+%221%2C+2%22+%29%2C+circle%28+1%2C+2%2C+0.15+%29+%29%2C%0D%0A++++green%28+locate%28+7%2C+4%2C+%227%2C+4%22+%29%2C+circle%28+7%2C+4%2C+0.15+%29+%29%0D%0A++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%280.333333333333333%29x+%2B+%281.66666666666667%29 ALIGN=MIDDLE  ALT=\"y=%280.333333333333333%29x+%2B+%281.66666666666667%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29x+%2B+1.66666666666667 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29x+%2B+1.66666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then inverse <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;\" > will be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29x+%2B+1.66666666666667 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29x+%2B+1.66666666666667\"   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" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2F3%29y+%2B+1.66666666666667 ALIGN=MIDDLE  ALT=\"x=%281%2F3%29y+%2B+1.66666666666667\"   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-1.66666666666667=%281%2F3%29y+ ALIGN=MIDDLE  ALT=\"x-1.66666666666667=%281%2F3%29y+\"   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=%28x-1.66666666666667%29%2F%281%2F3%29=y+ ALIGN=MIDDLE  ALT=\"%28x-1.66666666666667%29%2F%281%2F3%29=y+\"   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=3%28x-1.66666666666667%29=y+ ALIGN=MIDDLE  ALT=\"3%28x-1.66666666666667%29=y+\"   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=3x-5.00000000000001=y+ ALIGN=MIDDLE  ALT=\"3x-5.00000000000001=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=3x-5+ ALIGN=MIDDLE  ALT=\"y=3x-5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29=3x-5 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29=3x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "what is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28f%5E-1%283%29%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28f%5E-1%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >: first find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%283%29=3%2A3-5=9-5=4 ALIGN=MIDDLE  ALT=\"f%5E-1%283%29=3%2A3-5=9-5=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and plug it in\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28f%5E-1%283%29%29=f%5E-1%284%29=3%2A4-5=12-5=7 ALIGN=MIDDLE  ALT=\"f%5E-1%28f%5E-1%283%29%29=f%5E-1%284%29=3%2A4-5=12-5=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );