document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73977>Question 73977</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0471456535/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am having difficulty with this equation.<BR>\n" );
document.write( "Find the inverse of the function,\r<BR>\n" );
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document.write( " f(x) = (3 + 2x)/(2-5x)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52992 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=52992\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the inverse of a function, set the function equal to y , exchange the x's and the y, then solve for y. The given function is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%283%2B2x%29%2F%282-5x%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%283%2B2x%29%2F%282-5x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the function = y'<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2B2x%29%2F%282-5x%29 ALIGN=MIDDLE  ALT=\"y+=+%283%2B2x%29%2F%282-5x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Exchange the x's for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283%2B2y%29%2F%282-5y%29 ALIGN=MIDDLE  ALT=\"x+=+%283%2B2y%29%2F%282-5y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now solve for y. Multiply both sides by (2-5y)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%282-5y%29+=+3%2B2y ALIGN=MIDDLE  ALT=\"x%282-5y%29+=+3%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the left side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-5xy+=+3%2B2y ALIGN=MIDDLE  ALT=\"2x-5xy+=+3%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 5xy to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+3%2B5xy%2B2y ALIGN=MIDDLE  ALT=\"2x+=+3%2B5xy%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 3 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3+=+5xy%2B2y ALIGN=MIDDLE  ALT=\"2x-3+=+5xy%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor yhe y on the right side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3+=+y%285x%2B2%29 ALIGN=MIDDLE  ALT=\"2x-3+=+y%285x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by (5x+2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-3%29%2F%285x%2B2%29+=+y ALIGN=MIDDLE  ALT=\"%282x-3%29%2F%285x%2B2%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29+=+%282x-3%29%2F%285x%2B2%29 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29+=+%282x-3%29%2F%285x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Checking ths solution:<BR>\n" );
document.write( "We want to show that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28f%5E%28-1%29%28x%29%29+=+x ALIGN=MIDDLE  ALT=\"f%28f%5E%28-1%29%28x%29%29+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28%282x-3%29%2F%285x%2B2%29%29+=+%283%2B2%28%282x-3%29%2F%285x%2B2%29%29%29%2F%282-5%28%282x-3%29%2F%285x%2B2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the right side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28%282x-3%29%2F%285x%2B2%29%29+=+%28%283%285x%2B2%29%2B2%282x-3%29%29%2F%285x%2B2%29%29%2F%28%282%285x%2B2%29-5%282x-3%29%29%2F%285x%2B2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Continue to simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28%282x-3%29%2F%285x%2B2%29%29+=+%283%285x%2B2%29%2B2%282x-3%29%29%2F%282%285x%2B2%29-5%282x-3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28%282x-3%29%2F%285x%2B2%29%29+=+%2815x%2B6%2B4x-6%29%2F%2810x%2B4-10x%2B15%29 ALIGN=MIDDLE  ALT=\"f%28%282x-3%29%2F%285x%2B2%29%29+=+%2815x%2B6%2B4x-6%29%2F%2810x%2B4-10x%2B15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19x%2F19+=+x ALIGN=MIDDLE  ALT=\"19x%2F19+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Whew!!!<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28f%5E%28-1%29%28x%29%29+=+x ALIGN=MIDDLE  ALT=\"f%28f%5E%28-1%29%28x%29%29+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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