document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=153021>Question 153021</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the Inverse of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=3%2Bx%5E3+ ALIGN=MIDDLE  ALT=\"+f%28x%29=3%2Bx%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use Descarte's Rule of Signes to determine the number of positive and negative real zeros of the polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%28x%29+=+2x%5E4%2B3x%5E3-2x%5E2%2Bx-2+ ALIGN=MIDDLE  ALT=\"+p%28x%29+=+2x%5E4%2B3x%5E3-2x%5E2%2Bx-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > can have\r<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 #112472 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=112472\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2Bx%5E3 ALIGN=MIDDLE  ALT=\"y=3%2Bx%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2By%5E3 ALIGN=MIDDLE  ALT=\"x=3%2By%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Switch x and y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=y%5E3 ALIGN=MIDDLE  ALT=\"x-3=y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 3 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Cx-3%29=y ALIGN=MIDDLE  ALT=\"root%283%2Cx-3%29=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 3 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=root%283%2Cx-3%29 ALIGN=MIDDLE  ALT=\"y=root%283%2Cx-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the inverse function is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}\left(x\right)=\sqrt[3]{x-3}\">\r<BR>\n" );
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document.write( "# 2)\r<BR>\n" );
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document.write( "<h4>Positive Zeros:</h4>\r<BR>\n" );
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document.write( "First count the sign changes of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E4%2B3x%5E3-2x%5E2%2Bx-2 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E4%2B3x%5E3-2x%5E2%2Bx-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E4 ALIGN=MIDDLE  ALT=\"2x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E3 ALIGN=MIDDLE  ALT=\"3x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is no change in sign\r<BR>\n" );
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document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E3 ALIGN=MIDDLE  ALT=\"3x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2 ALIGN=MIDDLE  ALT=\"-2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is a sign change from positive to negative \r<BR>\n" );
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document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2 ALIGN=MIDDLE  ALT=\"-2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is a sign change from negative to positive \r<BR>\n" );
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document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is a sign change from positive to negative \r<BR>\n" );
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document.write( "So there are 3 sign changes for the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E4%2B3x%5E3-2x%5E2%2Bx-2 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E4%2B3x%5E3-2x%5E2%2Bx-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "So there are 3 or 1 positive zeros\r<BR>\n" );
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document.write( "<h4>Negative Zeros:</h4>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-x%29=2%28-x%29%5E4%2B3%28-x%29%5E3-2%28-x%29%5E2%2B%28-x%29-2 ALIGN=MIDDLE  ALT=\"f%28-x%29=2%28-x%29%5E4%2B3%28-x%29%5E3-2%28-x%29%5E2%2B%28-x%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now let's replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x ALIGN=MIDDLE  ALT=\"-x\"   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=f%28-x%29=2x%5E4-3x%5E3-2x%5E2-x-2 ALIGN=MIDDLE  ALT=\"f%28-x%29=2x%5E4-3x%5E3-2x%5E2-x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "Now let's count the sign changes of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-x%29=2x%5E4-3x%5E3-2x%5E2-x-2 ALIGN=MIDDLE  ALT=\"f%28-x%29=2x%5E4-3x%5E3-2x%5E2-x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E4 ALIGN=MIDDLE  ALT=\"2x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E3 ALIGN=MIDDLE  ALT=\"-3x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is a sign change from positive to negative \r<BR>\n" );
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document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E3 ALIGN=MIDDLE  ALT=\"-3x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2 ALIGN=MIDDLE  ALT=\"-2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is no change in sign\r<BR>\n" );
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document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2 ALIGN=MIDDLE  ALT=\"-2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x ALIGN=MIDDLE  ALT=\"-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is no change in sign\r<BR>\n" );
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document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x ALIGN=MIDDLE  ALT=\"-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is no change in sign\r<BR>\n" );
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document.write( "So there is 1 sign change for the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-x%29=2x%5E4-3x%5E3-2x%5E2-x-2 ALIGN=MIDDLE  ALT=\"f%28-x%29=2x%5E4-3x%5E3-2x%5E2-x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "So there is 1 negative zero<BR>\n" );
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