document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180066>Question 1180066</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If f(x) = ax+b/cx+d, x  ≠  -d/c, -a/c, find f^-1(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #809724 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=809724\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Take the given function<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28ax%2Bb%29%2F%28cx%2Bd%29 ALIGN=MIDDLE  ALT=\"y=%28ax%2Bb%29%2F%28cx%2Bd%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "To find the inverse, switch the x and y...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28ay%2Bb%29%2F%28cy%2Bd%29 ALIGN=MIDDLE  ALT=\"x+=+%28ay%2Bb%29%2F%28cy%2Bd%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "...and solve for the new y.<br><BR>\n" );
document.write( "I leave it to you to do that.<br><BR>\n" );
document.write( "This is a common type of problem, usually using numerical coefficients instead of a, b, c, and d, on high school math competitions.  There is a quick shortcut that is easily memorized to make this kind of problem easy to solve quickly:<br><BR>\n" );
document.write( "The inverse of the function<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28ax%2Bb%29%2F%28cx%2Bd%29 ALIGN=MIDDLE  ALT=\"y=%28ax%2Bb%29%2F%28cx%2Bd%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-dx%2Bb%29%2F%28cx-a%29 ALIGN=MIDDLE  ALT=\"y=%28-dx%2Bb%29%2F%28cx-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Note in the inverse function, compared to the original...<br><BR>\n" );
document.write( "the \"b\" and \"c\" coefficients remain in the same places, unchanged; and<BR>\n" );
document.write( "the \"a\" and \"d\" coefficients switch places and change sign.<br><BR>\n" );
document.write( "So of course if you solve for the new y algebraically, as suggested above, your answer should be<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-dx%2Bb%29%2F%28cx-a%29 ALIGN=MIDDLE  ALT=\"y=%28-dx%2Bb%29%2F%28cx-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );