document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62544>Question 62544</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I had this problem on a test.  I found the inverse function, but I got stuck on the checking.<BR>\n" );
document.write( "Find the inverse function for f(x)=4x-2/3x.  Check your answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #43312 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=43312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the inverse function for f(x)=4x-2/3x.  Check your answer.<BR>\n" );
document.write( "Let f(x)=y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284x-2%29%2F3x ALIGN=MIDDLE  ALT=\"y=%284x-2%29%2F3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Change the y's to x's and  the x's to y's.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284y-2%29%2F3y ALIGN=MIDDLE  ALT=\"x=%284y-2%29%2F3y\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%28x%29=%283y%29%284y-2%29%2F3y ALIGN=MIDDLE  ALT=\"3y%28x%29=%283y%29%284y-2%29%2F3y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3xy=4y-2 ALIGN=MIDDLE  ALT=\"3xy=4y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3xy-4y=-4y%2B4y-2 ALIGN=MIDDLE  ALT=\"3xy-4y=-4y%2B4y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3xy-4y=-2 ALIGN=MIDDLE  ALT=\"3xy-4y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%283x-4%29=-2 ALIGN=MIDDLE  ALT=\"y%283x-4%29=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%283x-4%29%2F%283x-4%29=-2%2F%283x-4%29 ALIGN=MIDDLE  ALT=\"y%283x-4%29%2F%283x-4%29=-2%2F%283x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%2F%283x-4%29 ALIGN=MIDDLE  ALT=\"y=-2%2F%283x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "let y=f^-1(x)<BR>\n" );
document.write( "f^-1(x)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F%283x-4%29 ALIGN=MIDDLE  ALT=\"-2%2F%283x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To check take the f(f^-1(x)) and f^-1(f(x)) if they equal x, then they are inverses. [This is taking the composite functions.  You substitute the functions into each other and simplify.  If this is completely foreign to you let me know and I'll explain this more thoroughly.]<BR>\n" );
document.write( "f(f^-1(x))=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%28-2%2F%283x-4%29%29-2%29%2F%283%28-2%2F%283x-4%29%29%29 ALIGN=MIDDLE  ALT=\"%284%28-2%2F%283x-4%29%29-2%29%2F%283%28-2%2F%283x-4%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-8%2F%283x-4%29-2%29%2F%28-6%2F%283x-4%29%29 ALIGN=MIDDLE  ALT=\"%28-8%2F%283x-4%29-2%29%2F%28-6%2F%283x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-4%29%28-8%2F%283x-4%29-2%29%2F%28%283x-4%29%28-6%2F%283x-4%29%29%29 ALIGN=MIDDLE  ALT=\"%283x-4%29%28-8%2F%283x-4%29-2%29%2F%28%283x-4%29%28-6%2F%283x-4%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-8-2%283x-4%29%29%2F-6 ALIGN=MIDDLE  ALT=\"%28-8-2%283x-4%29%29%2F-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-8-6x%2B8%29%2F-6 ALIGN=MIDDLE  ALT=\"%28-8-6x%2B8%29%2F-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x%2F-6 ALIGN=MIDDLE  ALT=\"-6x%2F-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Yes!!!! This means that they are very likely inverses, but to be thorough, check f^-1(f(x))<BR>\n" );
document.write( "f^-1(f(x))=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F%283%28%284x-2%29%2F3x%29-4%29 ALIGN=MIDDLE  ALT=\"-2%2F%283%28%284x-2%29%2F3x%29-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F%28%284x-2%29%2Fx-4%29 ALIGN=MIDDLE  ALT=\"-2%2F%28%284x-2%29%2Fx-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2F%28x%284x-2%29%2Fx-4%29%29 ALIGN=MIDDLE  ALT=\"-2x%2F%28x%284x-2%29%2Fx-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2F%284x-2-4x%29 ALIGN=MIDDLE  ALT=\"-2x%2F%284x-2-4x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2F-2 ALIGN=MIDDLE  ALT=\"-2x%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Yes!!! This means that we're right!!!!<BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );