document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=547261>Question 547261</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a couple that I am can not figure out <BR>\n" );
document.write( "thanks so much for your help\r<BR>\n" );
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document.write( "g(x)= sqrt 5x-4<BR>\n" );
document.write( "h(x)= 4x^2+7<BR>\n" );
document.write( "Find:  h(g(x))\r<BR>\n" );
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document.write( "g(x)=5x^2-4x<BR>\n" );
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document.write( "h(x)= sqrt x-7\r<BR>\n" );
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document.write( "find the domain of : g(h(x)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #356316 by </B><A HREF=/tutors/aboutme.mpl?userid=mathie123><B>mathie123(224)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathie123><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=356316\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> when we are trying to find h(g(x)), what we are doing is really just substituting g(x) for any x we see in h(x).  This means\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=4%28sqrt%285x-4%29%29%5E2%2B7 ALIGN=MIDDLE  ALT=\"h%28g%28x%29%29=4%28sqrt%285x-4%29%29%5E2%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since we need to do exponents first from BEDMAS, we know that the square root and the squared are opposites of each other, and therefore cancel each other out.  This leaves:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28g%28x%29%29=4%285x-4%29%2B7 ALIGN=MIDDLE  ALT=\"h%28g%28x%29%29=4%285x-4%29%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28g%28x%29%29=20x-16%2B7 ALIGN=MIDDLE  ALT=\"h%28g%28x%29%29=20x-16%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28g%28x%29%29=20x-9 ALIGN=MIDDLE  ALT=\"h%28g%28x%29%29=20x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So for the second part...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=5x%5E2-4x ALIGN=MIDDLE  ALT=\"g%28x%29=5x%5E2-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "     _______<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29=+sqrt%28x-7%29 ALIGN=MIDDLE  ALT=\"h%28x%29=+sqrt%28x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We need to first find g(h(x)).  Just as in the first question, we just substitute h(x) for any x we see in g(x).  <BR>\n" );
document.write( "This leaves:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=5%28sqrt%28x-7%29%29%5E2-4%28sqrt%28x-7%29%29 ALIGN=MIDDLE  ALT=\"g%28x%29=5%28sqrt%28x-7%29%29%5E2-4%28sqrt%28x-7%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=5%28x-7%29-4%28sqrt%28x-7%29%29 ALIGN=MIDDLE  ALT=\"g%28x%29=5%28x-7%29-4%28sqrt%28x-7%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now the domain just means to see if there is any value of x that will make the above formula not work. <BR>\n" );
document.write( "The first part of the formula (x-7) does not cause any problems. <BR>\n" );
document.write( "The second part however does.  We know that we cannot have a negative number under a square root (try it on your calculator... you will see it makes an error appear).\r<BR>\n" );
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document.write( "This means <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-7%3E=+0 ALIGN=MIDDLE  ALT=\"x-7%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=7 ALIGN=MIDDLE  ALT=\"x%3E=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "therefore the domain is any x such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=7 ALIGN=MIDDLE  ALT=\"x%3E=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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