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" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52987 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=52987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y=\frac{3+2x}{2-5x}\">Start with given equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x=\frac{3+2y}{2-5y}\">Switch the x and y variables<BR>\n" );
document.write( "Now solve for y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (2-5y)x=(\frac{3+2y}{2-5y})(\frac{2-5y}{1})\">Multiply both sides by (2-5y)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2x-5xy=3+2y\">Distribute the x on the left side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2x-3=2y+5xy\">Get all y terms to one side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2x-3=y(2+5x)\">Factor out a y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{2x-3}{2+5x}=y\frac{(2+5x)}{(2+5x)}\">Divide both sides by (2+5x)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y=\frac{-3+2x}{2+5x}\">Here's our inverse function. In other words<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f^{-1}(x)=\frac{-3+2x}{2+5x}\"><BR>\n" );
document.write( "<p><BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "If we let x=1 and plugged it into <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y=\frac{3+2x}{2-5x}\"> we would get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y=\frac{3+2}{2-5}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y=\frac{-5}{3}\"><BR>\n" );
document.write( "If we plug in  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{-5}{3}\"> in for x into our inverse equation <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y=\frac{-3+2x}{2+5x}\"> we should get y=1 out.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y=\frac{-3+2(-5/3)}{2+5(-5/3)}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y=\frac{-3-\frac{10}{3}}{2-\frac{25}{3}}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y=\frac{\frac{-9-10}{3}}{\frac{6-25}{3}}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y=\frac{\frac{-19}{3}}{\frac{-19}{3}}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y=\frac{-19}{3}{\frac{3}{-19}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y=1\">So this verifies that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y=\frac{-3+2x}{2+5x}\"> is our answer. Hope all of this makes sense. </SPAN>\n" );
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