document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159812>Question 1159812</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let  f(x)=(2x^2)/(x^2-1) and g(x)=e^(x^2-4).<BR>\n" );
document.write( "	Solve for x the equation g(x)=16.<BR>\n" );
document.write( "	Find f(g(x)). Simplify your answer.<BR>\n" );
document.write( "	Describe the domains of f(x) and g(x).<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 #782904 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=782904\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C%22%22%2Cf%28x%29=%282x%5E2%29%2F%28x%5E2-1%29+%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C%22%22%2Cf%28x%29=%282x%5E2%29%2F%28x%5E2-1%29+%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=matrix%282%2C1%2C%22%22%2Cg%28x%29=e%5E%28x%5E2-4%29%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C%22%22%2Cg%28x%29=e%5E%28x%5E2-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=16 ALIGN=MIDDLE  ALT=\"g%28x%29=16\"   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=matrix%282%2C1%2C%22%22%2C16=e%5E%28x%5E2-4%29%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C%22%22%2C16=e%5E%28x%5E2-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......take natural log of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C%22%22%2C4ln%282%29=%28x%5E2-4%29+ln%28e%29%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C%22%22%2C4ln%282%29=%28x%5E2-4%29+ln%28e%29%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=matrix%282%2C1%2C%22%22%2C4ln%282%29%2Fln%28e%29=%28x%5E2-4%29%29+ ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C%22%22%2C4ln%282%29%2Fln%28e%29=%28x%5E2-4%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%29=1 ALIGN=MIDDLE  ALT=\"ln%28e%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=x%5E2-4=4ln%282%29+ ALIGN=MIDDLE  ALT=\"x%5E2-4=4ln%282%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=x%5E2=4ln%282%29+%2B4 ALIGN=MIDDLE  ALT=\"x%5E2=4ln%282%29+%2B4\"   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=x%5E2=4%28ln%282%29+%2B1%29 ALIGN=MIDDLE  ALT=\"x%5E2=4%28ln%282%29+%2B1%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=x=sqrt%284%28ln%282%29+%2B1%29%29 ALIGN=MIDDLE  ALT=\"x=sqrt%284%28ln%282%29+%2B1%29%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=x=2sqrt%28ln%282%29+%2B1%29 ALIGN=MIDDLE  ALT=\"x=2sqrt%28ln%282%29+%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Simplify your answer.\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C%22%22%2Cf%28g%28x%29%29=f%28e%5E%28x%5E2-4%29%29%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C%22%22%2Cf%28g%28x%29%29=f%28e%5E%28x%5E2-4%29%29%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=matrix%282%2C1%2C%22%22%2Cf%28g%28x%29%29=%282%28e%5E%28x%5E2-4%29%29%5E2%29%2F%28%28e%5E%28x%5E2-4%29%29%5E2-1%29%29 ALIGN=MIDDLE   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=matrix%282%2C1%2C%22%22%2Cf%28g%28x%29%29=%282%28e%5E%282%28x%5E2-4%29%29%29%29%2F%28e%5E%282%28x%5E2-4%29%29-1%29%29 ALIGN=MIDDLE   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=matrix%282%2C1%2C%22%22%2Cf%28g%28x%29%29=%282e%5E%282x%5E2-8%29%29%2F%28e%5E%282x%5E2-8%29-1%29%29 ALIGN=MIDDLE   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=matrix%282%2C1%2C%22%22%2Cf%28g%28x%29%29=%282e%5E%282x%5E2-8%29%29%2F%28%28%28e%5E%28x%5E2%29+-+e%5E4%29%28e%5E%28x%5E2%29+%2B+e%5E4%29%29%2Fe%5E8%29%29 ALIGN=MIDDLE   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=matrix%282%2C1%2C%22%22%2Cf%28g%28x%29%29=%282e%5E%282x%5E2%29%29%2F%28%28e%5E%28x%5E2%29+-+e%5E4%29+%28e%5E%28x%5E2%29+%2B+e%5E4%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Describe the domains of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <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;\" >.\r<BR>\n" );
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document.write( "the domain of<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29 ALIGN=MIDDLE  ALT=\"+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=matrix%282%2C1%2C%22%22%2Cf%28x%29=%282x%5E2%29%2F%28x%5E2-1%29+%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C%22%22%2Cf%28x%29=%282x%5E2%29%2F%28x%5E2-1%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "domain will be all real numbers except values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > that make denominator equal to zero, so exclude those\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-1=0+ ALIGN=MIDDLE  ALT=\"x%5E2-1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=1+ ALIGN=MIDDLE  ALT=\"x%5E2=1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%281+%29 ALIGN=MIDDLE  ALT=\"x=sqrt%281+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "domain is:\r<BR>\n" );
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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;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-1 ALIGN=MIDDLE  ALT=\"x%3C%3E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E1 ALIGN=MIDDLE  ALT=\"x%3C%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > }\r<BR>\n" );
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document.write( "the domain of<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;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C%22%22%2Cg%28x%29=e%5E%28x%5E2-4%29%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C%22%22%2Cg%28x%29=e%5E%28x%5E2-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > (all real numbers)\r<BR>\n" );
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