document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=15349>Question 15349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In reference to Inverse Functions:  How do you determine when to use the \"short cut\" method when trying to find the inverse of a function?  For example, f(x) y = (x3+8)/3 so, we cubed it, added 8, and then divided by 3.  If you undo it in reverse order (multiply 3, minus 8, cube root) it becomes the inverse. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29+=+root%283%2C3x-8%29 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29+=+root%283%2C3x-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Why won't this work on all the problems? Thank you in advance!      </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #7618 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=7618\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  You are right for the inverse of<BR>\n" );
document.write( " f(x)= y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3%2B8%29%2F3 ALIGN=MIDDLE  ALT=\"%28x%5E3%2B8%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " to get <BR>\n" );
document.write( " y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%5E%28-1%29%28x%29+=+%283x-8%29%5E%281%2F3%29+ ALIGN=MIDDLE  ALT=\"+f%5E%28-1%29%28x%29+=+%283x-8%29%5E%281%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( " But use ^ for exponent and parentehsis for grouping terms next time. \r<BR>\n" );
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document.write( " If the original function is constructed by elementary invertible<BR>\n" );
document.write( " function (such as addition, multiplication,...) , we only need to<BR>\n" );
document.write( " apply reverse process step by step to get the inverse function.<BR>\n" );
document.write( "        <BR>\n" );
document.write( "  Since y=f(x)= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5Bk%5D ALIGN=MIDDLE  ALT=\"T%5Bk%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5Bk-1%5D ALIGN=MIDDLE  ALT=\"T%5Bk-1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5B1%5D%28x%29 ALIGN=MIDDLE  ALT=\"T%5B1%5D%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > then<BR>\n" );
document.write( "  <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;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5B1%5D%5E%28-1%29 ALIGN=MIDDLE  ALT=\"T%5B1%5D%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5B2%5D%5E%28-1%29 ALIGN=MIDDLE  ALT=\"T%5B2%5D%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5Bk%5D%5E%28-1%29%28x%29 ALIGN=MIDDLE  ALT=\"T%5Bk%5D%5E%28-1%29%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " (if each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5Bi%5D+ ALIGN=MIDDLE  ALT=\"T%5Bi%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is invertible.]\r<BR>\n" );
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document.write( " By for some functions such as y = x/(x^2+1) (or the functions containing<BR>\n" );
document.write( " some transcendental functions as trig or log ) <BR>\n" );
document.write( " is not so easy to get 1st inverse. I suggest that you try.<BR>\n" );
document.write( "  <BR>\n" );
document.write( " Anyway, you have got good idea and good luck!!!\r<BR>\n" );
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document.write( " Kenny\r<BR>\n" );
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