document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=316056>Question 316056</A>: <I><SPAN STYLE=\"word-break: break-all;\"> let g(x) = 1/x^2 and h(x)= 1/((sqrt x )- 1)<BR>\n" );
document.write( "please determine the the following function<BR>\n" );
document.write( "h(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 #226084 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=226084\">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=h%28x%29=1%2F%28sqrt%28x%29-1%29 ALIGN=MIDDLE  ALT=\"h%28x%29=1%2F%28sqrt%28x%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28g%28x%29%29=1%2F%28sqrt%281%2F%28x%5E2%29%29-1%29 ALIGN=MIDDLE  ALT=\"h%28g%28x%29%29=1%2F%28sqrt%281%2F%28x%5E2%29%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=1%2F%28x%5E2%29 ALIGN=MIDDLE  ALT=\"g%28x%29=1%2F%28x%5E2%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=h%28g%28x%29%29=1%2F%28sqrt%281%29%2Fsqrt%28x%5E2%29-1%29 ALIGN=MIDDLE  ALT=\"h%28g%28x%29%29=1%2F%28sqrt%281%29%2Fsqrt%28x%5E2%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28g%28x%29%29=1%2F%281%2Fsqrt%28x%5E2%29-1%29 ALIGN=MIDDLE  ALT=\"h%28g%28x%29%29=1%2F%281%2Fsqrt%28x%5E2%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 1 to get 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28g%28x%29%29=1%2F%281%2Fx-1%29 ALIGN=MIDDLE  ALT=\"h%28g%28x%29%29=1%2F%281%2Fx-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 'x' (this is assuming that 'x' is non-negative)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28g%28x%29%29=1%2F%281%2Fx-x%2Fx%29 ALIGN=MIDDLE  ALT=\"h%28g%28x%29%29=1%2F%281%2Fx-x%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the second '1' as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fx ALIGN=MIDDLE  ALT=\"x%2Fx\"   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=h%28g%28x%29%29=1%2F%28%281-x%29%2Fx%29 ALIGN=MIDDLE  ALT=\"h%28g%28x%29%29=1%2F%28%281-x%29%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the lower fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28g%28x%29%29=x%2F%281-x%29 ALIGN=MIDDLE  ALT=\"h%28g%28x%29%29=x%2F%281-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the reciprocal of the lower fraction.\r<BR>\n" );
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document.write( "So the composite function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28g%28x%29%29=x%2F%281-x%29 ALIGN=MIDDLE  ALT=\"h%28g%28x%29%29=x%2F%281-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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