document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1034949>Question 1034949</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this problem:<BR>\n" );
document.write( "Suppose <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 2x and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1 ALIGN=MIDDLE  ALT=\"f%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the inverse of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%283%29 ALIGN=MIDDLE  ALT=\"f%5E-1%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%5E-1%29 ALIGN=MIDDLE  ALT=\"%28f%5E-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%29 ALIGN=MIDDLE  ALT=\"%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #649893 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=649893\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E3+%2B2x+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E3+%2B2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28f%5E-1%28x%29%29+=+x+=+%28f%5E-1%28x%29%29%5E3+%2B+2f%5E-1%28x%29+ ALIGN=MIDDLE  ALT=\"f%28f%5E-1%28x%29%29+=+x+=+%28f%5E-1%28x%29%29%5E3+%2B+2f%5E-1%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > after plugging in the inverse <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the original equation.\r<BR>\n" );
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document.write( "Now differentiate implicitly wrt x.  \r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+3%2A%28f%5E-1%28x%29%29%5E2%2A%28df%5E-1%28x%29%2Fdx%29+%2B+2%28df%5E-1%28x%29%2Fdx%29+=++%283%2A%28f%5E-1%28x%29%29%5E2+%2B+2%29%28df%5E-1%28x%29%2Fdx%29++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E3+%2B2x+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E3+%2B2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%28x%29%2Fdx+=+3x%5E2+%2B2+%3E+0+ ALIGN=MIDDLE  ALT=\"df%28x%29%2Fdx+=+3x%5E2+%2B2+%3E+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all real x hence f(x) increasing ==> f(x) is one-to- DISABLED_event_one= => f(x) has an inverse function.  Incidentally, f(1) = 3, and so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%283%29+=+1 ALIGN=MIDDLE  ALT=\"f%5E-1%283%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=++%283%2A%28f%5E-1%283%29%29%5E2+%2B+2%29%28df%5E-1%283%29%2Fdx%29++ ALIGN=MIDDLE  ALT=\"1+=++%283%2A%28f%5E-1%283%29%29%5E2+%2B+2%29%28df%5E-1%283%29%2Fdx%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+%283%2A1%5E2+%2B+2%29%28df%5E-1%283%29%2Fdx%29+=+5%28df%5E-1%283%29%2Fdx%29 ALIGN=MIDDLE  ALT=\"1+=+%283%2A1%5E2+%2B+2%29%28df%5E-1%283%29%2Fdx%29+=+5%28df%5E-1%283%29%2Fdx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%5E-1%283%29%2Fdx+=+1%2F5 ALIGN=MIDDLE  ALT=\"df%5E-1%283%29%2Fdx+=+1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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