document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113796>Question 113796</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given f(x)=x^3+2 and g(x)=cube_root(x-2), show that f(g(x))=x and g(f(x))=x. Graph both functions on the same set of coordinate axes.<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 #82813 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=82813\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3%2B2 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with f(x)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=%28g%28x%29%29%5E3%2B2 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=%28g%28x%29%29%5E3%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=g%28x%29 ALIGN=MIDDLE  ALT=\"x=g%28x%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=f%28g%28x%29%29=%28root%283%2Cx-2%29%29%5E3%2B2 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=%28root%283%2Cx-2%29%29%5E3%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29 ALIGN=MIDDLE  ALT=\"g%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Cx-2%29 ALIGN=MIDDLE  ALT=\"root%283%2Cx-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is given since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=root%283%2Cx-2%29 ALIGN=MIDDLE  ALT=\"g%28x%29=root%283%2Cx-2%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=f%28g%28x%29%29=%28x-2%29%2B2 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=%28x-2%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cube the cube root (these two functions \"undo\" each other and cancel out)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=x ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "So this shows that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=x ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=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=g%28x%29=root%283%2Cx-2%29 ALIGN=MIDDLE  ALT=\"g%28x%29=root%283%2Cx-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with g(x)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28f%28x%29%29=root%283%2Cf%28x%29-2%29 ALIGN=MIDDLE  ALT=\"g%28f%28x%29%29=root%283%2Cf%28x%29-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=f%28x%29 ALIGN=MIDDLE  ALT=\"x=f%28x%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=g%28f%28x%29%29=root%283%2Cx%5E3%2B2-2%29 ALIGN=MIDDLE  ALT=\"g%28f%28x%29%29=root%283%2Cx%5E3%2B2-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Replace f(x) with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B2 ALIGN=MIDDLE  ALT=\"x%5E3%2B2\"   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=g%28f%28x%29%29=root%283%2Cx%5E3%29 ALIGN=MIDDLE  ALT=\"g%28f%28x%29%29=root%283%2Cx%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28f%28x%29%29=x ALIGN=MIDDLE  ALT=\"g%28f%28x%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Take the cube root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get x. Remember the cube root and the cube cancel each other out.\r<BR>\n" );
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document.write( "So this shows that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28f%28x%29%29=x ALIGN=MIDDLE  ALT=\"g%28f%28x%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now if we graph the two functions, we get\r<BR>\n" );
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